Elsevier

Discrete Mathematics

Volume 338, Issue 8, 6 August 2015, Pages 1481-1483
Discrete Mathematics

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Equitable partition of graphs into induced forests

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Abstract

An equitable partition of a graph G is a partition of the vertex-set of G such that the sizes of any two parts differ by at most one. We show that every graph with an acyclic coloring with at most k colors can be equitably partitioned into k1 induced forests. We also prove that for any integers d1 and k3d1, any d-degenerate graph can be equitably partitioned into k induced forests.

Each of these results implies the existence of a constant c such that for any kc, any planar graph has an equitable partition into k induced forests. This was conjectured by Wu, Zhang, and Li in 2013.

Keywords

Planar graphs
Arboricity
Acyclic coloring

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