2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 6366
author:  Tomasz Bartnicki, Jarosław Grytczuk and Hal Kierstead 

title:  The game of arboricity 
keywords:  
abstract: 
Using a fixed set of colors
C
, Ann and Ben color the edges of a graph
G
so that no monochromatic cycle may appear. Ann wins
if all edges of
G
have been colored, while Ben wins if completing a
coloring is not possible. The minimum size of
C
for which Ann has a winning strategy is called the
game arboricity of
G
, denoted by
A
. We prove that
g
(G)
A
for any graph
g
(G) ≤3k
G
of arboricity
k
, and that there are graphs such that
A
. 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.
g
(G)≥2k2

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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. 6366 
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