On the game coloring index of -decomposable graphs

Abstract The game coloring index col g ′ ( G ) of a graph G is the score of the edge marking game (the edge-coloring version of the marking game) on G when the two players use their best strategy. From Andres (2006), Cai and Zhu (2001) [ 5 ], Erdos et al. (2004) and Montassier et al. (2012), the game coloring index is at most Δ + 2 for the class of forests of maximum degree Δ , denoted F Δ . We prove that col g ′ ( G ) ≤ Δ ( G ) + 3 a − 1 for every graph G of arboricity a , i.e. every graph decomposable into a forests and we introduce a generalized decomposition of the well-known ( a , d ) - and F ( a , d ) -decompositions to improve this result. In particular, we improve bounds for some planar graphs.