On the game coloring index of F+-decomposable graphs

From Andres (2006), Cai and Zhu (2001) [5], Erdös 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 FΔ. We prove that colg′(G)≤Δ(G)+3a−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.