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Star list chromatic number of planar subcubic graphs

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Abstract

A proper coloring of the vertices of a graph G is called a star-coloring if the union of every two color classes induces a star forest. The graph G is L-star-colorable if for a given list assignment L there is a star-coloring π such that π(v)∈L(v). If G is L-star-colorable for any list assignment L with |L(v)|≥k for all v∈V(G), then G is called k-star-choosable. The star list chromatic number of G, denoted by \(\chi_{s}^{l}(G)\), is the smallest integer k such that G is k-star-choosable. In this paper, we prove that every planar subcubic graph is 6-star-choosable.

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Acknowledgements

The authors would like to thank the referees for their valuable suggestions that helped to improve this work. M. Chen’s research is supported by NSFC (No. 11101377). W. Wang’s research is supported by NSFC (No. 11071223), ZJNSFC (No. Z6090150), ZJIP (No. T200905), ZSDZZZZXK08 and IP-OCNS-ZJNU.

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Authors and Affiliations

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

    Min Chen & Weifan Wang

  2. LaBRI UMR CNRS 5800, Université Bordeaux I, 33405, Talence Cedex, France

    Min Chen & André Raspaud

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  1. Min Chen
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  2. André Raspaud
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  3. Weifan Wang
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Correspondence to Min Chen.

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Chen, M., Raspaud, A. & Wang, W. Star list chromatic number of planar subcubic graphs. J Comb Optim 27, 440–450 (2014). https://doi.org/10.1007/s10878-012-9522-7

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  • DOI: https://doi.org/10.1007/s10878-012-9522-7

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