Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-16T19:04:40.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Restricted Edge-colourings of Bipartite Graphs

Published online by Cambridge University Press:  12 September 2008

Roland Häggkvist
Roland Häggkvist
Affiliation:
Department of Mathematics, University of Umeå, S-90187, Umeå, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose each vertex of a bipartite multigraph (with partition (X, Y)) is assigned a set of colours; we say this colour scheme is feasible if the edges of the graph can be properly coloured so that each receives a colour in both of its endpoints' sets. We prove various results showing that certain types of colour scheme are always feasible. For instance, we prove that if the colour scheme obtained by assigning the set {1,…, d(x)} of colours to each vertex x of X and the set T = {1,…, t} (t < Δ(X)) to each vertex of Y is feasible, then so is every colour scheme where each vertex x of X gets d(x) colours from T and each vertex of Y gets the set T.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 385 - 392
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Galvin, F. (1995) The list-chromatic index of a bipartite multigraph. J. Combinatorial Theory (B) 63 153–158.CrossRefGoogle Scholar
[2]Fiorini, S. and Wilson, R. J. (1977) Edge-colourings of graphs. Research Notes in Mathematics 16. Pitman.Google Scholar
[3]Hilton, A. J. W. and Rodger, C. A. (1982) Edge-colouring regular bipartite graphs. Annals of Discrete Math. 13 139–158.Google Scholar
[4]Häggkvist, R. (1978) A solution of the Evans conjecture for latin squares of large size. Combinatorics János Bolyai Mathematical Society and North Holland, 495–513.Google Scholar
[5]Smetaniuk, B. (1981) A new construction on latin squares I. Proof of the Evans conjecture. Ars Comb. 11 155–172.Google Scholar
[6]Anderssen, L. D. and Hilton, A. J. W. (1983) Thank Evans! Proc. London Math. Soc. 47(3) 507–522.CrossRefGoogle Scholar
[7]Häggkvist, R. (1989) Decompositions of regular bipartite graphs. In: Surveys in Combinatorics 1989 (Siemens, J., ed.), LMS Lecture Series 141 115–147.Google Scholar