2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 375378
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
4
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. 375378 
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