Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T13:22:24.888Z Has data issue: false hasContentIssue false

List Colourings of Regular Hypergraphs

Published online by Cambridge University Press:  02 February 2012

DAVID SAXTON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail: D.W.Saxton@dpmms.cam.ac.uk, A.G.Thomason@dpmms.cam.ac.uk)
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail: D.W.Saxton@dpmms.cam.ac.uk, A.G.Thomason@dpmms.cam.ac.uk)

Abstract

We show that the list chromatic number of a simple d-regular r-uniform hypergraph is at least (1/2r log(2r2) + o(1)) log d if d is large.

Type
Paper
Copyright
Copyright © Cambridge University Press 2012

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]Alon, N. (1993) Restricted colorings of graphs. In Surveys in Combinatorics 1993, Vol. 187 of London Mathematical Society Lecture Notes (Walker, K., ed.), Cambridge University Press, pp. 133.Google Scholar
[2]Alon, N. (2000) Degrees and choice numbers. Random Struct. Alg. 16 364368.3.0.CO;2-0>CrossRefGoogle Scholar
[3]Alon, N. and Kostochka, A. Hypergraph list coloring and Euclidean Ramsey theory. Random Struct. Alg. (to appear).Google Scholar
[4]Alon, N. and Kostochka, A. Dense uniform hypergraphs have high list chromatic number. Discrete Mathematics, (in press).Google Scholar
[5]Erdős, P., Rubin, A. L. and Taylor, H. (1979) Choosability in graphs. In Proc. West Coast Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium XXVI 125157.Google Scholar
[6]Haxell, P. and Pei, M. (2009) On list coloring Steiner triple systems. J. Combin. Designs 17 314322.Google Scholar
[7]Haxell, P. and Verstraëte, J. (2010) List coloring hypergraphs. Electron. J. Combin. 17 #R129.CrossRefGoogle Scholar
[8]Saxton, D. and Thomason, A. In preparation.Google Scholar
[9]Vizing, V. G. (1976) Coloring the vertices of a graph in prescribed colors (in Russian). Diskret. Anal. 29 310.Google Scholar