Planar graphs without $5^{-}$-cycles at distance less than $3$ are $(\mathcal{I}, \mathcal{F})$-colorable Article Swipe
Related Concepts
Combinatorics
Planar graph
Vertex (graph theory)
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Mathematics
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Set (abstract data type)
Discrete mathematics
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Zhen He
,
Tao Wang
,
Xiaojing Yang
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.02969
· OA: W4388481890
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.02969
· OA: W4388481890
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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