The game of arboricity

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 $\textit{game arboricity}$ 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.
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Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.63-66, 2005, DMTCS Proceedings
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Tomasz Bartnicki, Jaroslaw Grytczuk, Hal Kierstead. The game of arboricity. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.63-66, 2005, DMTCS Proceedings. 〈hal-01184385〉

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