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arXiv · 1403.2810

Equitable vertex arboricity of planar graphs

Xin Zhang
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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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Xin Zhang. 2014-03-12. Equitable vertex arboricity of planar graphs. https://arxiv.org/abs/1403.2810

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