Planar graphs without $5^{-}$-cycles at distance less than $3$ are $(\mathcal{I}, \mathcal{F})$-colorable

Zhen He; Tao Wang; Xiaojing Yang

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arXiv · 2311.02969

Planar graphs without $5^{-}$-cycles at distance less than $3$ are $(\mathcal{I}, \mathcal{F})$-colorable

Zhen He·Tao Wang·Xiaojing Yang

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Abstract

A graph is $(\mathcal{I}, \mathcal{F})$-colorable if its vertex set can be partitioned into two subsets, one of which is an independent set, and the other induces a forest. In this paper, we prove that every planar graph without $5^{-}$-cycles at distance less than $3$ is $(\mathcal{I}, \mathcal{F})$-colorable.

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BibTeX RIS

Zhen He, Tao Wang, Xiaojing Yang. 2023-11-06. Planar graphs without $5^{-}$-cycles at distance less than $3$ are $(\mathcal{I}, \mathcal{F})$-colorable. https://arxiv.org/abs/2311.02969

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