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

Mickael Montassier 1 Arnaud Pêcher 1, 2 André Raspaud 1 Xuding Zhu 3
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
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Mickael Montassier, Arnaud Pêcher, André Raspaud, Xuding Zhu. Edge-partitions of sparse graphs and their applications to game coloring. 2009. ⟨hal-00368828⟩

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