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Short Proof of Galvin's Theorem on the List-chromatic Index of a Bipartite Multigraph

Published online by Cambridge University Press:  12 September 2008

Tomaž Slivnik
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK

Abstract

Recently, Galvin [7] proved that every k-edge-colourable bipartite multigraph is k-edge-choosable. In particular, for a bipartite multigraph G, . Here we give a brief self-contained proof of this result.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

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References

[1]Alon, N. and Tarsi, M. (1992) Colorings and orientations of graphs. Combinatorica 12 (2) 125134.CrossRefGoogle Scholar
[2]Bollobás, B. and Harris, A. J. (1985) List-colourings of graphs. Graphs and Combinatorics 1 115127.CrossRefGoogle Scholar
[3]Bollobás, B. and Hind, H. R. (1989) A new upper bound for the list chromatic number. Discrete Mathematics 74 6575.CrossRefGoogle Scholar
[4]Chetwynd, A. and Häggkvist, R. (1989) A note on list-colorings. J. Graph Theory 13 8795.CrossRefGoogle Scholar
[5]Erdős, P., Rubin, A. L. and Taylor, H. (1980) Choosability in graphs. Congressus Numerantium 26 125157.Google Scholar
[6]Gabow, H. N. (1976) Using Euler partitions to edge colour bipartite multigraphs. Int. J. Comput. Infor. Sci. 5 345355.CrossRefGoogle Scholar
[7]Galvin, F. (1995) The list chromatic index of a bipartite multigraph. J. Combinatorial Theory Series B 63 153158.CrossRefGoogle Scholar
[8]Gale, D. and Shapley, L. S. (1962) College admissions and the stability of marriage. Amer. Math. Monthly 69 915.CrossRefGoogle Scholar
[9]Häggkvist, R. and Janssen, J. (1993) On the list-chromatic index of bipartite graphs. Research Report No. 15, Department of Mathematics, University of Umeå.Google Scholar
[10]Häggkvist, R. and Janssen, J. (1993) New Bounds on the List-Chromatic Index of the Complete Graph and Other Simple Graphs. Research Report No. 19, Department of Mathematics, University of Umeå.Google Scholar
[11]Harris, A. J. (1985) Problems and conjectures in extremal graph theory. PhD dissertation, Cambridge.Google Scholar
[12]Janssen, J. C. M. (1993) Even and odd latin squares. PhD dissertation, Lehigh University.Google Scholar
[13]Janssen, J. C. M. (1993) The Dinitz problem solved for rectangles. Bull. Amer. Math. Soc. (New Series) 29 243249.CrossRefGoogle Scholar
[14]Kahn, J. (to appear) Asymptotically good list-colorings. J. Combinatorial Theory, Series A.Google Scholar
[15]Maffray, F. (1992) Kernels in perfect line-graphs. J. Combinatorial Theory, Series B 55 18.CrossRefGoogle Scholar
[16]Vizing, V. G. (1992) Colouring the vertices of a graph in prescribed colours (in Russian). Diskret. Analiz. 29 310.Google Scholar