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Acyclic 6-choosability of Planar Graphs without 5-cycles and Adjacent 4-cycles

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Abstract

A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v ∈ V(G)} with ∣L(v)∣ ≥ k for all v ∈ V(G), there exists a proper acyclic vertex coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V(G). In this paper, we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles, then G is acyclically 6-choosable.

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Acknowledgements

We are very grateful to the anonymous referees for their accurate suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, 524000, P. R. China

    Lin Sun

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  1. Lin Sun
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Correspondence to Lin Sun.

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Supported by Guangdong Province Basic and Applied Basic Research Foundation and Joint Foundation Project (Grant No. 2019A1515110324), Natural Science Foundation of Guangdong province (Grant No. 2019A1515011031), and University Characteristic Innovation Project of Guangdong province (Grant No. 2019KTSCX092)

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Sun, L. Acyclic 6-choosability of Planar Graphs without 5-cycles and Adjacent 4-cycles. Acta. Math. Sin.-English Ser. 37, 992–1004 (2021). https://doi.org/10.1007/s10114-021-9335-7

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  • DOI: https://doi.org/10.1007/s10114-021-9335-7

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