Asymptotics of the chromatic Index for multigraphs

Journal of Combinatorial Theory. Series B

Volumn 68, Issue 2, 1996, Pages 233-254

  Kahn, Jeff ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030295232     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.1996.0067     Document Type: Article

References (62)

1. 1. M. Ajtai, J. Komlós, and E. Szemerédi, A dense infinite Sidon sequence, European J. Combin. 2 (1981), 1-11.
2. 2. N. Alon, Restricted colorings of graphs, in "Surveys in Combinatorics, 1993" (Proc. 14th British Combinatorial Conf.), pp. 1-33, Cambridge Univ. Press, Cambridge, 1993.
3. 3. N. Alon and J. H. Spencer, "The Probabilistic Method," Wiley, New York, 1992.
4. 4. L. D. Andersen, On edge-colourings of graphs, Math. Scand. 40 (1977), 161-175.
5. 5. K. Azuma, Weighted sums of certain dependent random variables, Tokuku Math. J. 19 (1967), 357-367.
6. 6. J. van den Berg and J. E. Steif, Percolation and the hard-core lattice gas model, Stochastic Process. Appl. 49 (1994), 179-197.
7. 7. C. Berge, "Hypergraphs: Combinatorics of Finite Sets," North Holland, Amsterdam, 1989.
8. 8. K. Borsuk, Drei Sätze über die n-dimensionale euklidische Sphäre, Fundamenta Math. 20 (1933), 177-190.
9. 9. J. Edmonds, Maximum matching and a polyhedron with 0, 1-vertices, J. Res. Nat. Bureau Standards (B) 69 (1965), 125-130.
10. 10. P. Erdos, Some old and new problems in various branches of combinatorics, Cong. Numer. 23 (1979), 19-37.
11. 11. P. Erdos and L. Lovász, Problems and results on 3-chromatic hypergraphs and some related questions, Colloq. Math. Soc. János Bolyai 10 (1974), 609-627.
12. 12. P. Erdos, A. Rubin, and H. Taylor, Choosability in graphs, Cong. Numer. 26 (1979), 125-157.
13. 13. P. Erdos and J. Spencer, Lopsided Lovász Local Lemma and Latin transversals, Discr. Appl. Math. 30 (1990), 151-154.
14. 14. P. Frankl and V. Rödl, Near-perfect coverings in graphs and hypergraphs, European J. Combin. 6 (1985), 317-326.
15. 15. Z. Füredi, Matchings and covers in hypergraphs, Graphs Combin. 4 (1988), 115-206.
16. 16. F. Galvin, The list chromatic index of a bipartite multigraph, J. Combin. Theory Ser. B 63 (1995), 153-158.
17. 17. C. D. Godsil, Matchings and walks in graphs, J. Graph Theory 5 (1981), 285-297.
18. 18. M. K. Goldberg, On multigraphs of almost maximal chromatic class, Diskret. Analiz. 23 (1973), 3-7. [in Russian].
19. 19. M. K. Goldberg, Structure of multigraphs with restrictions on the chromatic class, Diskret. Analiz. 30 (1977), 3-12. [in Russian]
20. 20. M. K. Goldberg, Edge-colorings of multigraphs: recoloring technique, J. Graph Theory 8 (1984), 123-127.
21. 21. R. Häggkvist and J. C. M. Janssen, New bounds on the list-chromatic index of the complete graph and other simple graphs, unpublished manuscript.
22. 22. O. J. Heilmann and E. H. Lieb, Theory of monomer-dimer systems, Comm. Math. Phys. 25 (1972), 190-232.
23. 23. W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Stat. Assoc. 27 (1963), 13-30.
24. 24. I. J. Holyer, The NP-completeness of edge coloring, SIAM J. Comput. 10 (1981), 718-720.
25. 25. A. Johansson, An improved upper bound on the choice number for triangle free graphs, unpublished manuscript.
26. 26. J. Kahn, Coloring nearly-disjoint hypergraphs with n + o(n) colors, J. Combin. Theory Ser. A 59 (1992), 31-39.
27. 27. J. Kahn, Recent results on some not-so-recent hypergraph matching and covering problems, in "Extremal Problems for Finite Sets, Visegrád, 1991," pp. 305-353, Bolyai Soc. Math. Studies, Vol. 3, 1994.
28. 28. J. Kahn, Asymptotically good list-colorings, J. Combin. Theory Ser. A 73 (1996), 1-59.
29. 29. J. Kahn, On some hypergraph problems of Paul Erdos and the asymptotics of matchings, covers and colorings, in "The Mathematics of Paul Erdos," to appear.
30. 30. J. Kahn, A linear programming perspective on the Frankl-Rödl-Pippenger Theorem, Random Structures and Algorithms 8 (1996), 149-157.
31. 31. J. Kahn and P. M. Kayll, On hard-core distributions, Combinatorica, to appear.
32. 32. J. Kahn and P. M. Kayll, Fractional vs. integer covers in hypergraphs of bounded edge size, J. Combin. Theory Ser. A, to appear.
33. 33. J. Kahn and J. H. Kim, Random matchings in regular graphs, submitted for publication.
34. 34. P. M. Kayll, "Asymptotically Good Covers in Hypergraphs," thesis, Rutgers University, 1994.
35. 35. J. H. Kim, On Brooks' Theorem for sparse graphs, Combin. Probab. Comput. 4 (1995), 97-132.
36. 2/log t, Random Structures Algorithms 7 (1995), 173-207.
37. 37. J. Komlós, J. Pintz, and E. Szemerédi, A lower bound for Heilbronn's problem, J. London Math. Soc. 25 (1982), 13-24.
38. 38. D. König, Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, Math. Ann. 77 (1916), 453-465.
39. 39. D. König, Graphok és alkalmazásuk a determinánsok és a halmazok elméletére, Math. Termész. Ért. 34 (1916), 104-119.
40. 40. H. Kunz, Location of the zeros of the partition function for some classical lattice systems, Phys. Lett. A (1970), 311-312.
41. 41. M. Larsen, J. Propp, and D. Ullman, The fractional chromatic number of Mycielski's graphs, J. Graph. Theory 19 (1995), 411-416.
42. 42. C. W. Lee, Convex polytopes, the moment map, and canonical convex combinations, unpublished manuscript.
43. 43. D. Leven and Z. Galil, NP completeness of finding the chromatic index of regular graphs, J. Algorithms 4 (1983), 35-44.
44. 44. G. M. Louth, "Stochastic Networks: Complexity, Dependence and Routing," thesis, Cambridge University, 1990.
45. 45. L. Lovász, Kneser's conjecture, chromatic number and homotopy, J. Combin Theory 25 (1978), 319-324.
46. 46. L. Lovász and M. D. Plummer, "Matching Theory," North Holland, Amsterdam, 1986.
47. 47. V. Milman and G. Schechtman, "Asymptotic Theory of Finite Dimensional Normed Spaces," Springer, Berlin, 1980.
48. 48. T. Nishizeki and K. Kashiwagi, An upper bound on the chromatic index of multigraphs, in "Graph Theory with Applications to Algorithms and Computer Science" (Y. Alavi et al., Eds.), pp. 595-604, Wiley, New York, 1985.
49. 49. T. Nishizeki and K. Kashiwagi, On the 1.1 edge-coloring of multigraphs, SIAM J. Discrete Math. 3 (1990), 391-410.
50. 50. N. Pippenger and J. Spencer, Asymptotic behavior of the chromatic index for hypergraphs, J. Combin. Theory Ser. A 51 (1989), 24-42.
51. 51. Y. Rabinovich, A. Sinclair, and A. Wigderson, Quadratic Dynamical Systems, in "Proc. 33rd IEEE Symposium on Foundations of Computer Science," pp. 304-313, 1992.
52. 52. V. Rödl, On a packing and covering problem, European J. Combin. 5 (1985), 69-78.
53. 53. A. Schrijver, "Theory of Linear and Integer Programming," Wiley, Chichester, 1986.
54. 54. P. D. Seymour, Some unsolved problems on one-factorizations of graphs, in "Graph Theory and Related Topics" (Bondy and Murty, Eds.), Academic Press, New York, 1979.
55. 55. C. E. Shannon, A theorem on coloring the lines of a network, J. Math. Phys. 28 (1949), 148-151.
56. 56. J. Spencer, Lecture notes, M.I.T., 1987.
57. 57. J. Spencer, Asymptotic packing via a branching process, Random Structures and Algorithms 7 (1995), 167-172.
58. 58. B. Toft, 75 graph-colouring problems, in "Graph Colourings" (R. Nelson and R. J. Wilson, Eds.), pp. 9-35, Wiley, New York, 1990.
59. 59. V. G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz 3 (1964), 25-30. [in Russian]
60. 60. V. G. Vizing, The chromatic class of a multigraph, Kibernetica (Kiev) 3 (1965), 29-39; Cybernetics 3 (1965), 32-41.
61. 60. V. G. Vizing, The chromatic class of a multigraph, Kibernetica (Kiev) 3 (1965), 29-39; Cybernetics 3 (1965), 32-41.
62. 61. V. G. Vizing, Coloring the vertices of a graph in prescribed colors, Diskret. Analiz No. 29 Metody Diskret. Anal. v Teorii Kodov i Shem (1976), 3-10, 101 (MR58# 16371). [in Russian]