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ЛИТЕРАТУРА

1.1. Whitney Н., 2-Isomorphic Graphs., Am. J. Math., 55, 245—254 (1933).

1.2. Berge C., Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

1.3. Harary F. Graph Theory, Addison-Wesley, Reading, Mass., 1969. [Имеется перевод: Ф. Харари. Теория графов: — М.: Мир, 1973.]

1.4. J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan, London, 1976.

1.5. R. J. Wilson, Introduction to Graph Theory, Oliver and Boyed, Edinburgh, 1972. [Имеется перевод: P. Уилсон. Введение в теорию графов.— М.: Мир, 1977.]

1.6. С. L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York, 1968.

1.7. M. Behzad, G. Chartrand, Introduction to the Theory of Graphs, Allyn and Bacon, Boston, 1971.

1.8. N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, Englewood Cliffs, N.J., 1974.

2.1. S. Seshu, М. B. Reed, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, Mass., 1961.

2.2. М. B. Reed. The Seg: A New Class of Subgraphs, IRE Trans. Circuit Theory, Vol. CT-8, 17—22 (1961).

2.3. W. H. Kim, R. T. Chien, Topological Analysis and Synthesis of Communication Networks, Colombia University Press, New York, 1962.

2.4. W. K- Chen, Applied Graph Theory: Graphs and Electrical Networks, North-Holland, Amsterdam, 1971.

2.5. W. Mayeda, Graph Theory, Wiley-Interscience, New York, 1972.

2.6. H. Whitney, On the Abstract Properties of Linear Dependence, Am. J. Math., Vol. 57, 509—533 (1935).

2.7. C. St. J. A. Nash-Williams, Edge-Disjoint Spanning Trees of Finite Graphs, J. London Math. Soc., Vol. 36, 445—450 (1961).

2.8. W. T. Tutte, On the Problem of Decomposing a Graph into n Connected Factors, J. London Math. Soc., Vol. 36, 221—230 (1961).

2.9. R. L. Cummins, Hamilton Circuits in Tree Graphs, IEEE Trans. Circuit Theory, Vol. CT-13, 82-90 (1966).

3.1. V. Chvatal, On Hamilton’s Ideals, J. Combinatorial Theory B, Vol. 12, 163—168 (1972).

3.2. G. A. Dirac, Some Theorems on Abstract Graphs, Proc. London Math. Soc., Vol. 2, 69—81 (1952).

3.3. O. Ore, Arc Coverings of Graphs, Ann. Mat. Рига Appl., Vol. 55, 315—321 (1961).

3.4. L. Posa, A Theorem Concerning Hamilton Lines, Magyar Tud. Akad. Mat. Kutato Int. Kozl., Vol. 7, 225—226 (1962).

3.5. J. A. Bondy, Properties of Graphs with Constraints on Degrees, Studia Sci. Math. Hungar., Vol. 4 , 473—475 (1969).

3.6. C. L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York, 1968.

3.7. M. Behzad and G. Chartrand, Introduction to the Theory of Graphs, AHyn and Bacon, Boston, 1971.

3.8. S. Lin, Computer Solutions of the Traveling Salesman Problem, Bell Syst. Tech. J., Vol. 44, 2245—2269 (1965).

3.9. M. Belmore and G. L. Nemhauser, The Traveling Salesman Problem: A Survey, Operations Res., Vol. 16, 538—558 (1968).

3.10. M. Held and R. M. Karp, The Traveling Salesman Problem and Minimum Spanning Trees, Operations Res., Vol. 18, 1138—1162 (1970).

3.11. M. Held and R. M. Karp, The Traveling Salesman Problem and Minimum Spanning Trees: Part II, Math. Programming, Vol. 1, 6—25 (1971).

3.12. C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

3.13. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan, London, 1976, chap. 4.

3.14. C. St. J. A. Nash-Williams, Hamilton Arcs and Circuits, in Recent Trends in Graph Theory, Springer, Berlin, 1971, pp. 197—210.

3.15. J. A. Bondy and V. Chvatal, A Method in Graph Theorv, Discrete Math., Vol. 15, 111—135 (1976).

3.16. C. St. J. A. Nash-Williams, Hamiltonian Circuits, in Studies in Graph Theory, Part. II, MAA Press, 1975, pp. 301—360.

3.17. L. Lesniak-Foster, Some Recent Results in Hamiltonian Graphs, J. Graph Theory, Vol. 1, 27—36 (1977).

3.18. P. Erdos and T. Gallai, On Maximal Paths and Circuits of Graphs, Acta Math. Acad. Sci. Hung., Vol. 10, 337—356 (1959).

3.19. R. L. Cummins, Hamilton Circuits in Tree Graphs, IEEE Trans. Circuit Theory, Vol. CT-13, 82—90 (1966).

3.20. H. Shank, A Note on Hamilton Circuits in Tree Graphs, IEEE Trans. Circuit Theory, Vol. CT-15, 86 (1968).

4.1. S. MacLane and G. Birkhoff, Algebra, Macmillan, New York, 1967.

4.2. P. R. Halmos, Finite—Dimensional Vector Spaces, Van Nostrand Reinhold, New York, 1958.

4.3. F. E. Hohn, Elementary Matrix Algebra, Macmillan, New York, 1958.

4.4. W. K- Chen, On Vector Spaces Associated with a Graph, SIAM J. Appl. Math., Vol., 20, 526—529 (1971).

4.5. T. W. Williams and L. M. Maxwell, The Decomposition of a Graph and the Introduction of a New Class of Subgraphs, SIAM J. Appl. Math., Vol. 20, 385—389 (1971).

4.6. R. Gould, Graphs and Vectors Spaces, J. Math. Phys., Vol. 37, 193—214 (1958).

5.1. S. W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, 1967.

5.2. M. Hall, Jr., Combinarotial Theory, Blaisdell, Waltham, Mass., 1967.

5.3. T. Van Aardenne-Ehrenfest and N. G. de Bruijn, Circuits and Trees in Oriented Linear Graphs, Simon Stevin, Vol. 28, 203—217 (1951).

5.4. J. W. Moon, On Subtournaments of a Tournament, Canad. Math. Bull., Vol. 9, 297—301 (1966).

5.5. C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

5.6. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan, London, 1976.

5.7. M. G. Kendall, Further Contributions to the Theory of Paired Comparisons, Biometrics, Vol. 11, 43—62 (1955).

5.8. J. W. Moon and N. J. Pullman, On Generalized Tournament Matrices. SIAM Rev., Vol. 12, 384—389 (1970).

5.9. Ф. Харари Теория графов.—М.: Мир, 1973.

5.10. J. W. Moon, Topics on Tournaments, Holt, Rinehart and Winston, New York, 1968.

5.11. C. St. J. A. Nash-Williams, Hamiltonian Circuits, in Studies in Graph Theory, Part II, MAA Press, 1975, pp. 301—360.

5.12. D. E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Addison-Wesley, Reading Mass, 1968.

5.13. D. E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, Mass., 1973. [Имеется перевод: Д. E. Кнут. Искусство программирования для ЭВМ. т. 3: Сортировка и поиск:— М.: Мир, 1978.]

5.14. А. V. Aho, J. Е. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974. [Имеется перевод: A. Axo, Дж. Хопкрофт, Дж. Ульман. Построение и анализ вычислительных алгоритмов.— М.: Мир, 1979.]

5.15. Е. М. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practice, Prentice Hall, Englewood Cliffs, N.J., 1977. [Имеется перевод: Э. М. Рейнгольд, Ю. Нивергельт, Н. Дсо. Комбинаторные алгоритмы: Теория и практика: — М.: Мир, 1980.]

5.16. F. Нагагу, R. Z. Norman, and D. Cartwright, Structural Models: An Intro-duction to the Theory of Directed Graphs, Wiley, New York, 1965.

5.17. V. Chvatal and L. Lovasz, Every Directed Graph Has a Semi-Kernel, in Hypergraph Seminar (Eds. C. Berge and D. K- Ray-Chaudhuri), Springer, New York, 1974, p. 175.

6.1. F. E. Hohn, Elementary Matrix Algebra, Macmillan, New York, 1958.

6.2. W. K- Chen, Applied Graph Theory, North Holland, Amsterdam, 1971.

6.3. G. Kirchhoff, Uber die Auflosung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Strome geftihrt wird, Ann. Phys. Chem., Vol. 72, 497—508 (1947).

6.4. A. Cayley, A Theorem on Trees, Quart. J. Math., Vol. 23, 376—378 (1889).

6.5. J. W. Moon, Various Proofs of Cayley’s Formula for Counting Trees, in A Seminar on Graph Theory (Ed. F. Harary and L. W. Beinke), Holt, Rinehart and Winston, New York, 1967, pp. 70—78.

6.6. H. Priifer, Neuer Beweis eines Satzes fiber Permutationen, Arch. Math. Phys., Vol. 27, 742—744 (1918).

6.7. K- Sankara Rao, V. V. Bapeswara Rao, and V. G. K- Murti, Two—Three Admittance Products, Electron. Lett., Vol. 6, 834—835 (1970).

6.8. W. T. Tutte, The Dissection of Equilateral Triangles into Equilateral Triangles, Proc. Cambridge Phil. Soc., Vol. 44, 203—217 (1948).

6.9. F. Harary, The Determinant of the Adjacency Matrix of a Graph, SIAM Rev., Vol. 4, 202—210 (1962).

6.10. C. L. Coates. Flow-Graph Solutions of Linear Algebraic Equations IRE Trans., Circuit Theory, Vol. CT-6, 170—187 (1959).

6.11. S. J. Mason, Feedback Theory: Some Properties of Signal Flow Graphs, Proc. IRE., Vol. 41, 1144—1156 (1953).

6.12. S. J. Mason, Feedback Theory: Further Properties of Signal Flow Graphs,

Proc. IRE., Vol. 44, 920—926 (1956).

6.13. S. Seshu, М. B. Reed, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, Mass., 1961.

6.14. W. Mayeda, Graph Theory, Wiley-Interscience, New York, 1972.

6.15. N. Deo. Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, Englewood Cliffs, N.J., 1974.

6.16. F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York, 1973. [Имеется перевод: Ф. Харари, Е. Палмер. Перечисление графов: —М.: Мир, 1977.]

6.17. В. R. Myers, Number of Trees in a Cascade of 2-Port Networks, IEEE Trans. Circuit Theory, Vol CT-14, 284—290 (1967).

6.18. B. R. Myers, Number of Spanning Trees in a Wheel, IEEE Trans. Circuit Theory, Vol. CT-18, 280—282 (1971).

6.19. S. D. Bedrosian, Number of Spanning Trees in Multigraph Wheels, IEEE Trans. Circuit Theory, Vol. CT-19, 77—78 (1972).

6.20. N. K- Bose, R. Feick, and F. K- Sun, Genera! Solution to the Spanning Tret

Enumeration Problem in Multigraph Wheels, IEEE Trans. Circuit Theory, Vol. CT-20, 69—70 (1973).

6.21. M.N.S. Swamy and K- Thulasiraman, A Theorem in the Theory of Determinants and the Number of Spanning Trees of a Graph, Proc. IEEE Int. Symp. on Circuits and Systems, 153—156 (1976).

6.22. C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.

6.23. L.P.A. Robichaud, M. Boisvert, and J. Robert, Signal Flow Graphs and Applications, Prentice-Hall, Englewood Cliffs, N.J., 1962.

6.24. N. Balabanian and T. A. Bickart, Electrical Network Theory, Wiley, New York, 1969.

6.25. Y. Kajitani and S. Ueno, On the Rank of Certain Classes of Cutsets and Tie-Sets of a Graph, IEEE Trans. Circuits and Sys., Vol. CAS-26, 666—668 (1979).

7.1. K- Wagner, Bemerkungen zum Vierfarbenproblem, Ober Deutsh. Math. Verein, Vol. 46, 26—32 (1936).

7.2. I. Fary, On Straight Line Representation of Planar Graphs, Acta Sci. Math. Szeged, Vol. 11, 229—233 (1948).

7.3. S. K- Stein, Convex Maps, Proc. Am. Math. Soc., Vol. 2, 464—466 (1951).

7.4. H. Whitney, Non-Separable and Planar Graphs, Trans. Am. Math. Soc., Vol. 34 , 339—362 (1932).

7.5. C. Kuratowski, Sur le probleme des courbes gauches en topologie, Fund. Math., Vol. 15, 271—283 (1930).

7.6. Cm. [1.3].

7.7. W. T. Tutte, How to Draw a Graph, Proc. London Math. Soc., Vol. 13, 743—767 (1963).

7.8. K- Wagner, Uber eine Eigenschaft der ebenen Komplexe, Math. Ann., Vol. 114, 570—590 (1937).

7.9. F. Harary and W. T. Tutte, A Dual Form of Kuratowski’s Theorem, Canad. Math. Bull., Vol. 8, 17—20 (1965).

7.10. S. MacLane, A Structural Characterization of Planar Combinatorial Graphs, Duke Math. J., Vol. 3, 340—372 (1937).

7.11. H. Whitney, Planar Graphs, Fund. Math., Vol. 21, 73—84 (1933).

7.12. T. D. Parsons, On Planar Graphs, Am. Math. Monthly, Vol. 78, 176—178 (1971).

7.13. S. Seshu, М. B. Reed, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, Mass., 1961.

7.14. H. Whitney A Set of Topological Invariants for Graphs, Am. J. Math., Vol. 55, 231—235 (1933).

7.15. O. Ore, The Four Colour Problem, Academic Press, New York, 1967.

7.16. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications Macmillan, London, 1976.

7.17. J. E. Hopcroft and R. E. Tarjan, Efficient Planarity Testing, J. ACM, Vol. 21, 549—568 (1974).

7.18. N. K. Bose and K- A. Prabhu, Thickness of Graphs with Degree Constrained Vertices, IEEE Trans. Circuits and Sys., Vol. CAS—24, 184—190 (1975).

7.19. W. T. Tutte, On the Nonbiplanar Character of the Complete 9-graph, Canad. Math. Bull., Vol. 6, 319—330 (1963).

8.1. F. Harary The Maximum Connectivity of a Graph, Proc. Nat. Acad. Sci., U.S., Vol. 48, 1142—1146 (1962).

8.2. J. A. Bondy, Properties of Graphs with Constraints on Degrees, Studia Sci, Math. Hung., Vol. 4, 473—475 (1969).

8.3. G. Chartrand, A Graph Theoretic Approach to a Communication Problem, SIAM J. Appl. Math., Vol. 14, 778—781 (1966).

8.4. S. L. Hakimi, On the Realizability of a Set of Integers as Degrees of the Vertices of a Graph, SIAM J. Appl. Math., Vol. 10, 496—506 (1962).

8.5. V. Havel, A Remark on the Existence of Finite Graphs (in Hungarian), Casopois Pest. Mat., Vol. 80, 477—480 (1955).

8.6. D. L. Wang and D. L. Kleitman, On the Existence of «-Connected Graphs with Prescribed Degrees (n^s2), Networks, Vol. 3, 225—239 (1973).

8.7. P. Erdos and T. Gallai, Graphs with Prescribed Degrees of Vertices (in Hungarian), Mat. Lapok, Vol. 11, 264—274 (1960).

8.8. Cm. [1.3].

8.9. J. Edmonds, Existence of A-Edge-Connected Ordinary Graphs with Prescribed Degrees, J. Res. Nat. Bur. Stand. B., Vol. 68, 73—74 (1964).

8.10. D. L. Wang and D. J. Kleitman, A Note on n-Edge Connectivity, SIAM J. Appl. Math., Vol. 26, 313—314 (1974).

8.11. K- Menger, Zur allgemeinen Kurventheorie, Fund. Math., Vol. 10, 96—115 (1927).

8.12. H. Whitney, Congruent Graphs and the Connectivity of Graphs, Am. J. Math., Vol. 54, 150—168 (1932).

8.13. W. T. Tutte, A Theory of 3-Connected Graphs, Indag. Math., Vol. 23, 441—455 (1961).

8.14. L. R. Ford and D. R. Fulkerson, Maximal Flow Through a Network, Canad. J. Math., Voi. 8, 399—404 (1956).

8.15. P. Elias, A. Feinstein, С. E. Shannon, A Note on the Maximum Flow Through a Network, IRE Trans. Inform. Theory, IT-2, 117—119 (1956). [Имеется перевод: П. Элиас, А. Файнстейн, К- Шеннон. О максимальном потоке через сеть: В сб. К- Шеннон. Работы по теории информации и кибернетике: —М.: ИЛ, 1963.]

8.16. P. Hall, On Representatives of Subsets, J. London Math. Soc., Vol. 10, 26—30 (1935).

8.17. P. R. Halmosn, H. E. Vaughan, The Marriage Problem, Am. J. Math., Vol. 72, 214—215 (1950).

8.18. D. Konig, Graphs and Matrices, Mat. Fiz. Lapok, Vol. 38, 116—119 (1931).

8.19. O. Ore, Graphs and Matching Theorems, Duke Math J., Vol. 22 , 625—639 (1955).

8.20. R. Rado, Note on the Transfinite Case of Hall’s Theorem on Representatives, J. London Math. Soc., Vol. 42, 321—324 (1967).

8.21. C. Berge, Two Theorems in Graph Theory, Proc. Nat. Acad. Sci. U.S., Vol. 43, 842-844 (1957).

8.22. N.S. Mendelsohn, A. L. Dulmage, Some Generalizations of the Problem of Distinct Representatives, Canad, J. Math., Vol. 10, 230—241 (1958).

8.23. W. T. Tutte, The Factorization of Linear Graphs, J. London Math. Soc., Vol. 22, 107—111 (1947).

8.24. I. Anderson, Perfect Matchings of a Graph., J. Combinatorial Theory B., Vol. 10, 183-186 (1971).

8.25. L. Lovasz, Three Short Proofs in Graph Theory, J. Combinatorial Theory B, Vol. 19, 111—113 (1975).

8.26. C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.

8.27. F. T. Boesch (Ed.), Large-Scale Networks: Theory and Design, IEEE Press, New York, 1976.

8.28. S. L. Hakimi, An Algorithm for Construction of Least Vulnerable Communication Networks or the Graph with the Maximum Connectivity, IEEE Trans. Circuit Theory, Vol. CT-16, 229—230 (1969).

8.29. F. T. Boesch and R. E. Thomas, On Graphs of Invulnerable Communication Nets, IEEE Trans. Circuit Theory, Vol. CT-17, 183—192 (1970).

8.30. A. T. Amin and S. L. Hakimi, Graphs with Given Connectivity and Independence Number or Networks with Given Measures of Vulnerability and Survivability, IEEE Trans. Circuit Theory, Vol. CT-20, 2—10 (1973).

8.31. H. Frank and I. T. Frisch, Communication, Transmission, and Transsorta-tion Networks, Addison-Wesley, Reading, Mass., 1971.

8.32. L. Mirsky and H. Perfect, Systems of Representatives, J. Math. Anal. Applic., Vol. 15, 520—568 (1966).

8.33. R. A. Brualdi, Transversal Theory and Graphs, in Studies in Graph Theory, Part II, MAA Press, 1975, pp. 23—88.

8.34. L. Mirsky, Transversal Theory, Academic Press, New York, 1971.

8.35. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmil-lan, London, 1976. 8.36. Cm. [1.5].

9.1. D. Konig, Graphs and Matrices (in Hungarian), Mat. Fiz. Lapok, Vol. 38, 116—118 (1931).

9.2. C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

9.3. T. Gallai, Uber extreme Punkt und Kantenmengen, Ann. Univ. Sci. Budapest, Edtvos Sect. Math., Vol. 2, 133—138 (1959).

9.4. V- G. Vizing, On an Estimate of the Chromatic Class of a p-Graph (in Russian), Diskret. Analiz., Vol. 3, 25—30 (1964).

9.5. J. C. Fournier, Colorations des aretes d’un graphe, Cahiers du CERO, Vol. 15, 311—314 (1973).

9.6. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan, London, 1976.

9.7. R. L. Brooks, On Colouring the Nodes of a Network, Proc. Cambridge Phil. Soc., Vol. 37, 194—197 (1941).

9.8. L. S. Melnikov and V. G. Vizing, New Proof of Brooks’ Theorem, J. Combinatorial Theory, Vol. 7, 289—290 (1969).

9.9. L. Lovasz, Three Short Proofs in Graph Theory, J. Combinatorial Theory B, Vol. 19, 111—113 (1975).

9.10. P. J. Heawood, Map Colour Theorems, Quart. J. Math., Vol. 24, 332—338 (1890).

9.11. K. I. Appel and W. Haken, Every Planar Map is Four-Colorable, Bull. Am. Math. Soc., Vol. 82, 711—712 (1976).

9.12. O. Ore, The Four-Color Problem, Academic Press, New York, 1967.

S. 13. T. L. Saaty, Thirteen Colorful Variations on Guthrie’s Four-Color Conjecture, Am. Math. Monthly, Vol. 79, 2—43 (1972).

9.14. T. L. Saaty and P. C. Kainen, The Four-Coior Problem: Assaults and Conquests, McGraw-Hill, New York, 1977.

9.15. H. Whitney and W. T. Tutte, Kempe Chains and the Four Colour Problem, in Studies in Graph Theory, Part II, MAA Press, 1975, pp. 378—413.

9.16. Cm. [1.3].

9.17. P. Turan, An Extremal Problem in Graph Theory (in Hungarian), Mat. Fiz. Lapok, Vol. 48, 436—452 (1941).

9.18. P. Erdos, On the Graph Theorem of Turan (in Hungarian), Mat. Lapok, Vol. 21, 249—251 (1970).

9.19. B. Bollobas, Extremal Graph Theory, Academic Press, New York, 1978.

9-20 H. Frank and I. T. Frisch, Communication, Transmission, and Transportation Networks, Addison-Wesley, Reading, Mass., 1971.

9.21. F. T. Boesch (Ed.), Large-Scale Networks: Theory and Design, IEEE Press, New York, 1976.

9.22. P. Karivaratharajan and K- Thulasiraman, К-Sets of a Graph and Vulnerability of Communication Nets, Matrix and Tensor Quart., Vol. 25, 63—66 (1974), 77—86 (1975).

9.23. P. Karivaratharajan and K. Thulasiraman, An Extremal Problem in Graph Theory and Its Applications, Proc. IEEE Intl. Symp. on Circuits and Systems, Tokyo, Japan, 1979.

9.24. C. L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York, 1968.

9.25. L. Lovasz, On the Shannon Capacity of a Graph, IEEE Trans. Inform. Theory, Vol. IT-25, 1—7 (1979).

9.26. R. C. Read, An Introduction to Chromatic Polynomials, J. Combinatorial Theory, Vol. 4, 52—71 (1968).

9.27. G. D. Birkhoff, A Determinan Formula for the Number of Ways of Coloring a Map, Ann. Math., Vol. 14, 42—46 (1912).

9.28. W. T. Tutte, On Chromatic Polynomials and the Golden Ratio, J. Combinatorial Theory, Vol. 9, 289—296 (1970).

9.29. W. T. Tutte, Chromials in Studies in Graph Theory, Part II, MAA Press, 1975, pp. 361—377.

9.30. D. C. Wood, A Technique for Colouring a Graph Applicable to Large-Scale Timetabling Problems, Computer J., Vol. 12, 317 (1969).

9.31. N. Christofides, Graph Theory: An Algorithmic Approach, Academic Press, New York, 1975. [Имеется перевод: H. Крис'тофидес. Теория графов: Алгоритмический подход: — М.: Мир, 1978.]

9.32. Е. J. Cockayne and S. Т. Hedetniemi, Towards a Theory of Domination in Graphs, Networks, Vol. 7, 247—267 (1977).

9.33. E. J. Cockayne, S. T. Hedetniemi, Optimal Domination in Graphs, IEEE Trans. Circuits and Sys., Vol. CAS-22, 41—44 (1975).

9.34. D.J.A. Welsh, М. B. Powell, An Upper Bound for the Chromatic of a Graph and Its Application of Timetabling Problems, Computer J., Vol. 10, 85—87 (1967).

10.1. H. Whitney, On the Abstract Properties of Linear Dependence, Am. J. Math., Vol. 57, 509—533 (1935).

10.2. G. J. Minty, On the Axiomatic Foundations of the Theories of Directed Linear Graphs, Electrical Networks and Network Programming, J. Math, and Mech., Vol. 15, 485—520 (1966).

10.3. W. T. Tutte, Introduction to the Theory of Matroids, American Elsevier, New York, 1971.

10.4. D.J.A. Welsh, Matroid Theory, Academic Press, New York, 1976.

10.5. G. J. Minty, Monotone Networks, Proc. Roy. Soc., A, Vol. 257, 191—212 (1960).

10.6. G. J. Minty, Solving Steady-State Non-Linear Networks of ‘Monotone’ Elements, IRE Trans. Circuit Theory, Vol. CT-8, 99—104 (1961).

10.7. J. B. Kruskal, On the Shortest Spanning Subgraph of a Graph and the Travelling Salesman Problem, Proc. Am. Math. Soc., Vol. 7, 48—49 (1956).

10.8. R. Rado, Note on Independence Functions, Proc. London Math. Soc., Vol. 7, 300—320 (1957).

10.9. J. Edmonds, Matroids and the Greedy Algorithm, Math. Programming, Vol. 1, 127—136 (1971).

10.10. D. Gale, Optimal Assignments in an Ordered Set: An Application of .Matroid Theory, J. Combinatorial Theory, Vol. 4, 176—180 (1968).

10.11. D.J.A. Welsh, Kruskal’s Theorem for Matroids, Proc. Cambridge Phil. Soc., Vol. 64, 3—4 (1968).

10.12. Rabe von Randow, Introduction to the Theory of Matroids, Springer Lecture Notes in Mathematical Economics, Vol. 109, 1975.

10.13. C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

10.14. Cm. [1.5].

10.15. R. Rado, A Theorem on Independence Relations, Quart, J. Math. (Oxford), Vol. 13, 83—89 (1942).

10.16. A. Lehman, A Solution of the Shannon Switching Game, SIAM J. Appl. Math., Vol. 12, 687—725 (1964).

10.17. W. T. Tutte, A Homotopy Theorem for Matroids-I and II, Trans. Am. Math. Soc., Vol. 88, 144—174 (1958).

10.18. W. T. Tutte, Lectures on Matroids, J. Res. Nat. Bur. Stand., Vol. 69B, 1—48 (1965).

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10.20. W. T. Tutte, Connectivity in Matroids, Canad. J. Math., Vol. 18, 1301 — 1324 (1966).

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14.55. R. М. Karp, Reducibility among Combinatorial Problems, in Comoicxity of Computer Computations (R. E. Miller and J. W. Thatcher, Eds.) Plenum Press, New York, 1972, pp. 85—104. [Имеется перевод: P. М. Карп. Сводимость комбинаторных задач: Кибернетический сборник. Вып. 13: — М.: Мир, 1981.]

14.56. М. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, Freeman, San Francisco, Ca., 1979.

14.57. E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms, Computer Science Press, Potomac, Md., 1978.

14.58. А. V. Aho, М. R. Garey, and J. D. Ullman, The Transitive Reduction of a Directed Graph, SIAM J. Computing, Vol. 1, 131 —137 (1972).

14.59. H. Priifer, Neuer Beveis eines Satzes liber Permutationen, Arch. Match. Phys., Vol. 27, 742—744 (1918).

15.1. L. R. Ford and D. R. Fullkerson, Flows in Networks, Princeton Univ. Press, Princeton, N- J. 1962. [Имеется перевод: Л. P. Форд, Д. Фалкерсоп. Потоки в сетях: — М.: Мир, 1966.]

15.2. Е. W. Dijkstra, A Note on Two Problems in Connexion with Graphs, N timer ische Math., Vol. 1, 269—271 (1959).

15.3. D. B. Johnson, A Note on Dijkstra’s Shortest Path Algorithm, J. ACM, Vol. 20, 385—388 (1973).

15.4. J. Edmonds and R. M. Karp, Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems, J. ACM, Vol. 19, 248—264 (1972).

15.5. S. E. Dreyfus, An Appraisal of Some Shortest-Path Algorithms, Operations Research, Vol. 17, 395—412 (1969).

15.6. Т. C. Hu, A Decomposition Algorithm for Shortest Paths in a Network, Operations Research, Vol. 16, 91 —102 (1968).

15.7. H. Frank and I. T. Frisch, Communication, Transmission and Transportation Networks, Addison-Wesley, Reading, Mass., 1971.

15.8. Cm. [9.31].

15.9. E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.

15.10. P. M. Spira and A. Pan, On Finding and Updating Spanning Trees and Shortest Paths, SIAM J. Comput., Vol. 4, 375—380 (1975).

15.11. D. B. Johnson, Efficient Algorithms for Shortest Paths in Sparse Networks, J. ACM, Vol. 24, 1 — 13 (1977).

15.12. R. A. Wagner, A Shortest Path Algorithm for Edge-Snarse Graphs, J. ACM, Vol. 23, 50—57 (1976).

15.13. R. W. Floyd, Algorithm 97: Shortest Path, Comm. ACM, Vol. 5, 345 (1962).

15.14. Y. Tabourier, All Shortest Distances in a Graph: An Improvement to Dan-tzig’s Inductive Algorithm, Discrete Math., Vol. 4, 83—87 (1973).

15.15. J. Y. Yen, Finding the Lengths of All Shortest Paths in A'-Node, Non-Negative Distance Complete Networks Using A,3/2 Additions and N3 Comparisons, J. ACM, Vol. 19 , 423—424 (1972).

15.16. T. A. Williams and G. P. White, A Note on Yen’s Algorithm for Finding the Length of All Shortest Paths in A'-Node Non-Negative Distance Networks, J. ACM, Vol. 20, 389—390 (1973).

15.17. A. R. Pierce, Bibliography on Algorithms for Shortest Path, Shortest Spanning Tree and Related Circuit Routing Problems (1956—1974), Networks, Vol. 5, 129—149 (1975).

15.18. D. A. Huffman, A Method for the Construction of Minimum Redundancy Codes, Proc. IRE, Vol. 40, 1098—1101 (1952).

15.19. E. N. Gilbert and E. F. Moore, Variable-Length Binary Encodings, Bell Sys. Tech. J., Vol. 38, 933—968 (1959).

15.20. D. E. Knuth, Optimum Binary Search Trees, Acta Informatica, Vol. 1, 14—25 (1971).

15.21. A. Itai, Optimal Alphabetic Trees, SIAM J. Comput., Vol. 5, 9—18 (1976).

15.22. Т. C. Hu and A. C. Tucker, Optimal Computer Search Trees and Variable-Length Alphabetical Codes, SIAM J. Appl. Math., Vol. 21, 514—532 (1971).

15.23. Т. C. Hu, A New Proof of the T-C Algorithm, SIAM J. Appl. Math., Vol. 25, 83—94 (1973).

15.24. Cm. [5.12].

15.25. A. M. Garsia and M. L. Wachs, A New Algorithm for Minimum Cost Binary Trees, SIAM J. Comput., Vol. 6, 622—642 (1977).

15.26. Cm. [5.15].

15.27. M. Miyakawa, Т. Yuba, Y. Sugito, and M. Hoshi, Optimum Sequence Tree’s, SIAM J. Comput., Vol. 6, 201—234 (1977).

15.28. J. Edmonds, Paths, Trees and Flowers, Canad. J. Math., Vol. 17, 449—467 (1965).

15.29. H. N. Gabow, An Efficient Implementation of Edmonds’ Algorithm for Maximum Matching on Graphs, J. ACM, Vol. 23, 221—234 (1976).

15.30. М. I. Balinski, Labelling to Obtain aMaximum Matching, in Combinatorial Mathematics and Its Applications (R. C. Bose and T. A. Dowling, Eds ), Univ. North Carolina Press Chappel Hill, N.C., 1967, pp. 585—602.

15.31. D. Witzgall and С. T. Zahn, Jr., Modification of Edmonds’ Algorithm for Maximum Matching of Graphs, J. Res. Nat. Bur. Std., Vol. 69B, 91—98 (1965).

15.32. T. Kameda and I.Munro, AO(] V| • [/?() Algorithm for Maximum Matching of Graphs, Computing, Vol. 12, 91—98 (1974).

15.33. J. Edmonds, Maximum Matching and a Polyhedron with 0,1 Vertices, J. Res. Nat. Bur. Std., Vol. 69B, 125—130 (1965).

15.34. H. Gabow, An Efficient Implementation of Edmonds’ Maximum Matching Algorithm, Tech. Rep. 31, Stanford Univ. Comp. Science Dept., 1972.

15.35. J. A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan, London, 1976.

15.36. J. E. Hopcroft and R. M. Karp, An nls Algorithm for Maximum Matching in Bipartite Graphs, SIAM J. Comput., Vol. 2, 225—231 (1913).

15.37. S. Even and R. E. Tarjan, Network Flow and Testing Graph Connectivity, SIAM J. Comput., Vol. 4, 507—518 (1975).

15.38. S. Even and O. Kariv, An 0(п/г) Algorithm for Maximum Matching in General Graphs, Proc. 16th Annual Symp. on Foundations of Comp. Science. IEEE, 1975, pp. 100—112.

15.39. A. Itai, M. Rodeh, and S. L. Tanimoto, Some Matching Problems for Bipartite Graphs, J. ACM, Vol. 25, 517—525 (1978).

15.40. H. W. Kuhn, The Hungarian Method for the Assignment Problem, Naval Res. Legist. Quart., Vol. 2, 83—97 (1955).

15.41. J. Munkres, Algorithms for the Assignment and Transportation Problems, J. SIAM, Vol. 5, 32—38 (1957).

15.42. N. Megido, A. Tamir, An 0(N log N) Algorithm for a Class of Matching Problems, SIAM J. Comput., Vol. 7, 154—157 (1978).

15.43. S. Even, A. Itai, A. Shamir, On the Complexity of Time-Table and Multicommodity Flow Problems, SIAM J. Comput., Vol. 5, 691—703 (1976).

15.44. L. R. Ford, D. R. Fulkerson, Maximal Flow through a Network, Canad. J. Math., Vol. 8, 399—404 (1956).

15.45. P. Elias, A. Feinstein, С. E. Shannon, A Note on the Maximum Flow Through a Network, IRE Trans. Inform. Theory, IT-2, 117—119 (1956).

15.46. C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.

15.47. N. Zadeh, Theoretical Efficiency of the Edmonds-Karp Algorithm for Computing Maximal Flows, J. ACM, Vol. 19, 184—192 (1972).

15.48. Диниц E. А. Алгоритм решения задачи о максимальном потоке в сети с оценкой мощности, ДАН, 1970, т. 11, с. 1277—1280.

15.49. Карзанов А. В. Определение максимального потока в сети методом предикатов, ДАН, 1974, т. 15, с. 434—437.

15.50. V. М. Maihotra, М. Pramodh Kumar, and S. N. Maheswari, An 0(V3) Algorithm for Maximum Flows in Networks, Information Processing Lett., 7, 277—278 (1978).

15.51. S. Even, Graph Algorithms, Computer Press, Potomac, Md. 1979.

15.52. C. Berge, A. Ghouila-Houri, Programming, Games and Transportation Networks, Wiley, New Y'ork, 1962.

15.53. Т. C. Hu, Integer Programming and Network Flows, Addison-Wesley, Reading, Mass., 1969.

15.54. J. Edmonds, Optimum Branchings, J. Res. Nat. Bur. Std., Vol. 71B, 233— 240 (1967).

15.55. R. M. Karp, A Simple Derivation of Edmonds’ Algorithms for Optimum Branchings, Networks, Vol. 1, 265—272 (1972).

15.56. R. E. Tarjan, Finding Optimum Branchings, Networks, 7, 25—35 (1977).

15.57. Y. Chu, T. Liu, On the Shortest Arborescencef of a Directed Graph, Sci-entla Sinica (Peking), Vol. 4, 1396—1400 (1965); Math. Rev., Vol. 33, 1245 (G. W. Walkup).

15.53. F. C. Bock, An Algorithm to Construct a Minimum Directed Spanning Tree in a Directed Network, in Developments in Operati'ons Research, (B. Avi-Itzak, Ed.), Gordon and Breach, New York, 1971, pp. 29—44.

15.59. D. G. Corneil and С. C. Gotlieb, An Efficient Algorithm for Graph Isomorphism J. ACM, Vol. 17, 51—64 (1970).

15.60. L. Weinberg, A Simple and Efficient Algorithm for Determining Isomorphism of Planar Triply Connected Graphs, IEEE Trans. Circuit Theory, Vol. CT-13, 142—148 (1966).

15.61. J. E. Hopcroft and R. E. Tarjan, A V log V Algorithm for Isomorphism of Triconnected Planar Graphs, J. Comput. Syst. Sci., Vol. 7, 323—331 (1973).

15.62. J. E. Hopcroft and J. K- Wong, Linear Time Algorithm for Isomorphism on Planar Graphs, Proc. 6th Annual ACM Symp. on Theory of Computing, 1974, pp. 172—184.

15.63. J. E. Hopcroft and R, E. Tarjan, Efficient Planarity Testing, J. ACM, Vol. 21, 549—568 (1974).

15.64. N. Deo, Note on Hopcroft and Tarjan’s Planarity Algorithm, J. ACM, Vol. 23 , 74—75 (1976).

15.65. J. E. Hopcroft and R. E. Tarjan, Dividing a Graph into Triconnected Components, SIAM J. Comput., Vol. 2, 135—158 (1973).

15.66. D. J. Kleitman, Methods for Investigating the Connectivity of Large Graphs, IEEE Trans. Circuit Theory, Vol. CT-16, 232—233 (1969).

15.67. S. Even, An Algorithm for Determining whether the Connectivity of a Graph is at Least k, SIAM J. Comput., Vol. 4 , 393—396 (1975).

15.68. D. G. Corneil and B. Graham, An Algorithm for Determining the Chromatic Number of a Graph, SIAM J, Comput., Vol. 2, 311—318 (1973).

15.69. C. McDiarmid, Determining the Chromatic Number of a Graph, SIAM J. Comput., Vol. 8, 1—14 (1979).

15.70. D.J.A. Welsh and М. B. Powell, An Upper Bound for the Chromatic Number of a Graph and Its Applications to Timetabling Problems, The Computer J., Vol. 10, 85—86 (1967).

15.71. D. C. Wood, A Technique for Colouring a Graph Applicable to Large Scale Timetabling Problems, The Computer J., Vol. 10, 317—319 (1969).

15.72. D. Matula, G. Marble, and J. Isaacson, Graph Colouring Algorithms, in Graph Theory and Computing (R. C. Read, Ed.), Academic Press, New York, 1972, pp. 109—122.

15.73. D. Brelaz, New Methods to Color the Vertices of a Graph, Comm. ACM, Vol. 22, 251—256 (1979).

15.74. М. C. Pauli and S. H, Unger, Minimizing the Number of States in Incompletely Specified Sequential Switching Functions, IRE Trans. Elect. Comput., Vol. EC-8 , 356—357 (1959).

15.75. C. Bron and J. Kerbosch, Finding All Cliques of an Undirected Graph — Algorithm 457, Comm. ACM, Vol. 16, 575—577 (1973).

15.76. E. A. Akkoyunld, The Enumeration of Maximal Cliques of Large Graphs, SIAM J. Comput., Vol. 2, 1—6 (1973),

15.77. S. Tsukiyama, M. Ide, H. Ariyoshi, and I. Shirakawa, A New Algorithm for Generating All the Maximal Independent Sets, SIAM J. Comput., Vol. 6, 505-517 (1977).

15.78. R. E Tarjan and A. E. Trojanowski, Finding a Maximum Independent Set, SIAM J. Comput., Vol. 6, 537—546 (1977).

15.79. V. Chvatal, Determining the Stability Number of a Graph, SIAM J. Comput., Vol. G, 643—662 (1977).

15.80. J. B. Kruskal, Jr., On the Shortest Spanning Subtree of a Graph and the Travelling Salesman Problem, Proc. Am. Math. Soc., Vol. 7, 48—50 (1956).

15.81. R. C. Prim, Shortest Connection Networks and Some Generalizations, Bell Sys. Tech. J., Vol. 36, 1389—1401 (1957).

15.82. A. Kerschenbaum and R. Van Slyke, Computing Minimum Spanning Trees Efficiently, Proc. 25th Ann. Conf. of the ACM, 1972, 518—527.

15.83. A. C. Yao, An 0(|?|log log|K|) Algorithm for Finding Minimum Spanning Trees, Information Processing Lett., Vol., 4, 21—23 (1975).

15.84. D. Cheriton and R. E. Tarjan, Finding Minimum Spanning Trees, SIAM J. Comput., Vol. 5, 724—742 (1976).

15.85. H. N. Gabow, Two Algorithms for Generating Spanning Trees in Order, SIAM J. Comput., Vol. 6, 139—150 (1977).

15.86. K- P. Esqaran and R. E. Tarjan, Augmentation Problems, SIAM J. Comput., Vol. 5, 653—665 (1976).

15.87. A. Rosenthal and A. Goldner, Smallest Augmentations to Biconnect a Graph, SIAM J. Comput., Vol. 6, 55—66 (1977).

15.88. E. Reghbati and D. G. Corneil, Parallel Computations in Graph Theory, SIAM J. Comput., Vol. 7, 230—237 (1978).

15.89. J. Edmonds, Edge-Disjoint Branching, in Combinatorial Algorithms (R. Rustin, Ed.), Algorithmics Press, New York, 1973, pp. 91—§6.

15.90. D. R. Fulkerson and G. C. Harding, On Edge-Disjoint Branchings, Networks, Vol. 6, 97—104 (1976).

15.91. R. E. Tarjan, Edge-Disjoint Spanning Trees and Depth-First Search, Acta Informatica, Vol. 6, 171—185 (1976).

15.92. L. Lovasz, On Two Minimax Theorems in Graph, J. Combinatorial Theory B, Vol. 21, 96—103 (1976).

15.93. B. L. Golden and T. L. Magnanti, Deterministic Network Optimization: A Bibliography, Networks, Vol. 7, 149—183 (1977).

15.94. M. Fujii, T. Kasami, and K. Ninomiya, Optimal Sequencing of Two Equivalent Processors, SIAM J. Appl. Math., Vol. 17, 784—789 (1969); Erratum, Vol. ?0, 141 (1971).

15.95. E. G. Coffman, Jr., and R. L. Graham, Optimal Scheduling for Two-Processor Systems, Acta Informatica, Vol. 1, 200—213 (1972).

15.96. E. G. Coffman, Jr., and P. J. Denning, Operating System Theory, Prentice Hall, Englewood Cliffs, N.J., 1973.

15.97. R. Sethi, Scheduling Graphs on Two Processors, S/ЛМ J. Comput., Vol. 5, 73—82 (1976).

15.98. R. Sethi, Algorithms for Minimal Length Schedules, in Computers and Job Scheduling Theory (E. G. Coffman, Jr., Ed.), Wiley, New York, 1976, pp. 51—99.

15.99. J. D. Ullman Complexity of Sequencing Problems, in Computer and Job Scheduling Theory (E. G. Coffman, Jr., Ed.), Wiley, New York, 1976, pp. 139—164.

15 100. S. Lam and R. Sethi, Worst Case Analysis of Two Scheduling Algorithms, SIAM J. Comput., Vol. 6, 518—536 (1977).

15.101. D. J. Rose, A Graph-Theoretic Study of Numerical Solutions of Sparse Positive Definite Systems of Linear Equations, in Graph Theory and Computing (R. C. Read, Ed.), Academic Press, New York, 1972, pp. 183—217.

15.102. T. Ohtsuki, A Fast Algorithm for Finding an Optimal Ordering for Vertex Elimination on a Graph, SIAM J. Comput., Vol. 5, 133—145 (1976).

15.103. D. J. Rose, R. E. Tarjan, and G. S. Lueker, Algorithmic Aspects of Vertex Elimination on Graphs, S/ЛУИ J. Comput., Vol. 5, 266—283 (1976).

15.104. R. E. Tarjan, Graph Theory and Gauss Elimination, in Sparse Matrix Computations (J. R. Bunch and D. J. Rose, Eds.), Academic Press, New York, 1976,

15.105. E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms, Computer Science Press, Potcmac, Md., 1978.

15.106. M. R. Garey and D. S. Johnson, Approximation Algorithms for Combinatorial Problems: An Annotated Bibliography, in Algorithms and Complexity: New Directions and Recent Results (J. Traub, Ed.), Academic Press, New York, 1976.

15.107. G. B. Djntzig, All Shortest Routes in a Graph, in Theory of Graphs, Gordon and Breach, New York. 1967, pp. 91—92.

15.108. S. Even, Algorithmic Combinatorics, Macmillan, New York, 1973,

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