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arXiv · 2106.00159

Planar graphs without short even cycles are near-bipartite

Runrun Liu·Gexin Yu
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Abstract

A graph is {\em near-bipartite} if its vertex set can be partitioned into an independent set and a set that induces a forest. It is clear that near-bipartite graphs are $3$-colorable. In this note, we show that planar graphs without cycles of lengths in $\{4, 6, 8\}$ are near-bipartite.

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Runrun Liu, Gexin Yu. 2021-06-01. Planar graphs without short even cycles are near-bipartite. https://arxiv.org/abs/2106.00159

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