The game of arboricity
2005 ◽
Vol DMTCS Proceedings vol. AE,...
(Proceedings)
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Keyword(s):
International audience 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 $\textit{game arboricity}$ of $G$, denoted by $A_g(G)$. We prove that $A_g(G) \leq 3k$ for any graph $G$ of arboricity $k$, and that there are graphs such that $A_g(G) \geq 2k-2$. 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.
2015 ◽
Vol Vol. 17 no. 1
(Graph Theory)
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Keyword(s):
2005 ◽
Vol DMTCS Proceedings vol. AE,...
(Proceedings)
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Keyword(s):
2019 ◽
Vol 11
(01)
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pp. 1950004
2010 ◽
Vol DMTCS Proceedings vol. AM,...
(Proceedings)
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Keyword(s):
2012 ◽
Vol Vol. 14 no. 2
(Graph Theory)
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Keyword(s):
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2008 ◽
Vol Vol. 10 no. 3
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Keyword(s):
2008 ◽
Vol DMTCS Proceedings vol. AI,...
(Proceedings)
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Keyword(s):
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