List edge and list total colourings of multigraphs

Journal of Combinatorial Theory. Series B

Volumn 71, Issue 2, 1997, Pages 184-204

  Borodin, O V ^a   Kostochka, A V ^a   Woodall, D R ^b  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031280748     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.1997.1780     Document Type: Article

References (32)

1. M. Behzad, 1965, Graphs and Their Chromatic Numbers.
2. Bollobás B., Hind H. R. A new upper bound for the list chromatic number. Discrete Math. 74:1989;65-75.
3. O. V. Borodin, 1977, Criterion of chromaticity of a degree prescription, Abstracts of IV All-Union Conference on Theoretical Cybernetics, 127, 128.
4. O. V. Borodin, 1979, Problems of Colouring and of Covering the Vertex Set of a Graph by Induced Subgraphs, Novosibirsk.
5. Borodin O. V. On the total coloring of planar graphs. J. Reine Angew. Math. 394:1989;180-185.
6. Borodin O. V. An extension of Kotzig's theorem and the list edge colouring of planar graphs. Mat. Zametki. 48:1990;22-28.
7. O. V. Borodin, A. V. Kostochka, D. R. Woodall, Total colourings of planar graphs with large girth.
8. O. V. Borodin, A. V. Kostochka, D. R. Woodall, Total colourings of planar graphs with large maximum degree, J. Graph Theory.
9. Chen D. L., Wu J. L. The total coloring of some graphs. Combinatorics Graph Theory, Algorithms, and Applications, Beijing, 1993. 1994;World Science, River Edge. p. 17-20.
10. Erdos P., Rubin A. L., Taylor H. Choosability in graphs. Congr. Numer. 26:1979;125-157.
11. Galvin F. The list chromatic index of a bipartite multigraph. J. Combin. Theory Ser. B. 63:1995;153-158.
12. Gupta R. P. The chromatic index and the degree of a graph. Notices Amer. Math. Soc. 13:1966;abstract 66T-429.
13. Häggkvist R., Chetwynd A. Some upper bounds on the total and list chromatic numbers of multigraphs. J. Graph Theory. 16:1992;503-516.
14. Häggkvist R., Janssen J. New bounds on the list-chromatic index of the complete graph and other simple graphs. Res. Rep. 19:1993.
15. Hind H. R. Ph.D. thesis. 1988.
16. Jensen T. R., Toft B. Graph Coloring Problems. 1995;Wiley-Interscience, New York.
17. Kahn J. Recent results on some not-so-recent hypergraph matching and covering problems. Extremal Problems for Finite Sets, Visegrád, 1991. Bolyai Society Math. Studies. 3:1994;János Bolyai Math. Soc. Budapest. p. 305-353.
18. Kahn J. Asymptotically good list-colorings. J. Combin. Theory Ser. A. 73:1996;1-59.
19. J. Kahn, Asymptotics of the list-chromatic index for multigraphs.
20. Kostochka A. V. An analogue of shannon's estimate for complete colorings. Metody Diskret Anal. 30:1977;13-22.
21. Kostochka A. V. The total coloring of a multigraph with maximal degree 4. Discrete Math. 17:1977;161-163.
22. A. V. Kostochka, Exact upper bound for the total chromatic number of a graph, Proc. 24th International Wiss. Koll, Tech. Hochsch. Ilmenau, 1979, 33, 36.
23. Kostochka A. V. The total chromatic number of any multigraph with maximum degree five is at most seven. Discrete Math. 162:1996;199-214.
24. Rosenfeld M. On the total coloring of certain graphs. Israel J. Math. 9:1971;396-402.
25. Shannon C. E. A theorem on coloring the lines of a network. J. Math. Phys. 28:1948;148-151.
26. Slivnik T. A short proof of Galvin's theorem on the list-chromatic index of a bipartite multigraph. Combin. Probab. Comput. 5:1996;91-94.
27. Tutte W. T. The factors of graphs. Canad. J. Math. 4:1952;314-328.
28. Vijayaditya N. On total chromatic number of a graph. J. London Math. Soc. (2). 3:1971;405-408.
29. Vizing V. G. On an estimate of the chromatic class of ap. Metody Diskret Anal. 3:1964;25-30.
30. Vizing V. G. Critical graphs with given chromatic class. Metody Diskret Analiz. 5:1965;9-17.
31. Vizing V. G. Some unsolved problems in graph theory. Uspekhi Mat. Nauk. 23:1968;117-134.
32. Vizing V. G. Vertex colorings with given colors. Metody Diskret. Anal. 29:1976;3-10.