Abstract
AbstractLet be a graph. If the vertex set can be partitioned into two nonempty subsets and such that and are graphs with maximum degree at most and , respectively, then we say that has a ‐partition. A similar definition can be given for the notation ‐partition if is a forest with maximum degree at most , where . The maximum average degree of is defined to be mad. In this paper, we prove that every graph with mad admits an ‐partition. As a corollary, every graph with low genus and girth at least 6 admits an ‐partition. This improves a result of Borodin and Kostochka saying that every graph with mad admits a ‐partition.
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