Edge-partitions of sparse graphs and their applications to game coloring

Mickael Montassier (1) , Arnaud Pêcher (1, 2) , André Raspaud (1) , Xuding Zhu (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
3 Department of Applied Mathematics [Kaohsiung]

In this note, we prove that every graph with maximum average degree less than $\frac{32}{13}$ (resp. $\frac{30}{11}$, $\frac{32}{11}$, $\frac{70}{23}$) admits an edge-partition into a forest and a subgraph of maximum degree 1 (resp. 2, 3, 4). This implies that these graphs have game coloring number at most 5, 6, 7, 8, respectively.

Domaines: Mathématique discrète [cs.DM]

Mickael Montassier, Arnaud Pêcher, André Raspaud, Xuding Zhu. Edge-partitions of sparse graphs and their applications to game coloring. 2009. ⟨hal-00368828⟩