Equitable vertex arboricity of planar graphs

Xin Zhang

paper

Equitable vertex arboricity of planar graphs

arXiv:1403.2810

Abstract

Let $G_{1}$ be a planar graph such that all cycles of length at most 4 are independent and let $G_{2}$ be a planar graph without 3-cycles and adjacent 4-cycles. It is proved that the set of vertices of $G_{1}$ and $G_{2}$ can be equitably partitioned into $t$ subsets for every $t \geq 3$ so that each subset induces a forest. These results partially confirm a conjecture of Wu, Zhang and Li.

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