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

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DMTCS Conference vol AE (2005), pp. 341-344


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

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 341-344

author: Robert Berke and Tibor Szabó
title: Relaxed Two-Coloring of Cubic Graphs
keywords: Vertex coloring, bounded size components
abstract: We show that any graph of maximum degree at most
has a two-coloring, such that one color-class is an independent set while the other color induces monochromatic components of order at most
. On the other hand for any constant
we exhibit a
-regular graph, such that the deletion of any independent set leaves at least one component of order greater than
. Similar results are obtained for coloring graphs of given maximum degree with
colors such that
parts form an independent set and
parts span components of order bounded by a constant. A lot of interesting questions remain open.
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reference: Robert Berke and Tibor Szabó (2005), Relaxed Two-Coloring of Cubic Graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 341-344
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