DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 375-378


2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 375-378

author: Gábor Simonyi and Gábor Tardos
title: Local chromatic number and topology
keywords: graph coloring, topological method, Schrijver graphs, Mycielski graphs, surface quadrangulation
abstract: The local chromatic number of a graph, introduced by Erdős et al. in [EFHKRS], is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph. This talk, based on the papers [ST1, ST2, ST3], would like to survey some of our recent results on this parameter. We give a lower bound for the local chromatic number in terms of the lower bound of the chromatic number provided by the topological method introduced by Lovász. We show that this bound is tight in many cases. In particular, we determine the local chromatic number of certain odd chromatic Schrijver graphs and generalized Mycielski graphs. We further elaborate on the case of
-chromatic graphs and, in particular, on surface quadrangulations.
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reference: Gábor Simonyi and Gábor Tardos (2005), Local chromatic number and topology, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 375-378
bibtex: For a corresponding BibTeX entry, please consider our BibTeX-file.
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