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A note on the minimum number of choosability of planar graphs

Author

Listed:
  • Huijuan Wang

    (Qingdao University)

  • Lidong Wu

    (University of Texas at Tyler)

  • Xin Zhang

    (Xidian University)

  • Weili Wu

    (Taiyuan University of Technology
    University of Texas at Dallas)

  • Bin Liu

    (Ocean University of China)

Abstract

The problem of minimum number of choosability of graphs was first introduced by Vizing. It appears in some practical problems when concerning frequency assignment. In this paper, we study two important list coloring, list edge coloring and list total coloring. We prove that $$\chi '_{l}(G)=\varDelta $$ χ l ′ ( G ) = Δ and $$\chi ''_{l}(G)=\varDelta +1$$ χ l ′ ′ ( G ) = Δ + 1 for planar graphs with $$\varDelta \ge 8$$ Δ ≥ 8 and without adjacent 4-cycles.

Suggested Citation

  • Huijuan Wang & Lidong Wu & Xin Zhang & Weili Wu & Bin Liu, 2016. "A note on the minimum number of choosability of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1013-1022, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9805-2
    DOI: 10.1007/s10878-014-9805-2
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    References listed on IDEAS

    as
    1. Xiangwen Li & Vicky Mak-Hau & Sanming Zhou, 2013. "The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 716-736, May.
    2. Patrizio Angelini & Fabrizio Frati, 2012. "Acyclically 3-colorable planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 116-130, August.
    3. S. Bessy & F. Havet, 2013. "Enumerating the edge-colourings and total colourings of a regular graph," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 523-535, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Huijuan Wang & Panos M. Pardalos & Bin Liu, 2019. "Optimal channel assignment with list-edge coloring," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 197-207, July.
    2. Huijuan Wang & Bin Liu & Ling Gai & Hongwei Du & Jianliang Wu, 2018. "Minimum choosability of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 13-22, July.

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