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

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DMTCS Conference vol AE (2005), pp. 63-66


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

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 63-66

author: Tomasz Bartnicki, Jarosław Grytczuk and Hal Kierstead
title: The game of arboricity
abstract: Using a fixed set of colors
, Ann and Ben color the edges of a graph
so that no monochromatic cycle may appear. Ann wins if all edges of
have been colored, while Ben wins if completing a coloring is not possible. The minimum size of
for which Ann has a winning strategy is called the game arboricity of
, denoted by
. We prove that
(G) ≤3k
for any graph
of arboricity
, and that there are graphs such that
. The upper bound is achieved by a suitable version of the activation strategy, used earlier for the vertex coloring game. We also provide other strategie based on induction.
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reference: Tomasz Bartnicki and Jarosław Grytczuk and Hal Kierstead (2005), The game of arboricity, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 63-66
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