[hal-01184385] The game of arboricity

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 \emphgame arboricity of G, denoted by A_g(G). We prove that A_g(G) ≤3k for any graph G of arboricity k, and that there are graphs such that A_g(G)≥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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