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Acyclic 6-choosability of planar graphs without adjacent short cycles

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Abstract

A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycles. Given a list assignment L = {L(v) | v ∈ V} of G, we say that G is acyclically L-colorable if there exists a proper acyclic coloring π of G such that π(v) ∈ L(v) for all v ∈ V. If G is acyclically L-colorable for any list assignment L with |L(v)| ⩾ k for all v ∈ V (G), then G is acyclically k-choosable. In this paper, we prove that every planar graph G is acyclically 6-choosable if G does not contain 4-cycles adjacent to i-cycles for each i ∈ {3, 4, 5, 6}. This improves the result by Wang and Chen (2009).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    WeiFan Wang, Ge Zhang & Min Chen

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  1. WeiFan Wang
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  2. Ge Zhang
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  3. Min Chen
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Correspondence to WeiFan Wang.

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Wang, W., Zhang, G. & Chen, M. Acyclic 6-choosability of planar graphs without adjacent short cycles. Sci. China Math. 57, 197–209 (2014). https://doi.org/10.1007/s11425-013-4572-6

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