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Planar graphs with $$\Delta =9$$Δ=9 are neighbor-distinguishing totally 12-colorable

Author

Listed:
  • Weifan Wang

    (Zhejiang Normal University)

  • Jingjing Huo

    (Hebei University of Engineering)

  • Danjun Huang

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

Abstract

The neighbor-distinguishing total coloring of a graph G is a proper total coloring of G using k colors such that any two adjacent vertices have different sets of colors. It was known that every planar graph G with $$\Delta \ge 10$$Δ≥10 is neighbor-distinguishing totally $$(\Delta +3)$$(Δ+3)-colorable. In this paper, we extend this result to the case $$\Delta =9$$Δ=9. Namely, we prove that every planar graph G with $$\Delta =9$$Δ=9 is neighbor-distinguishing totally 12-colorable.

Suggested Citation

  • Weifan Wang & Jingjing Huo & Danjun Huang & Yiqiao Wang, 2019. "Planar graphs with $$\Delta =9$$Δ=9 are neighbor-distinguishing totally 12-colorable," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 1071-1089, April.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:3:d:10.1007_s10878-018-0334-2
    DOI: 10.1007/s10878-018-0334-2
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    References listed on IDEAS

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    1. Weifan Wang & Danjun Huang, 2014. "The adjacent vertex distinguishing total coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 379-396, February.
    2. Xiaohan Cheng & Guanghui Wang & Jianliang Wu, 2017. "The adjacent vertex distinguishing total chromatic numbers of planar graphs with $$\Delta =10$$ Δ = 10," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 383-397, August.
    3. Yiqiao Wang & Weifan Wang, 2010. "Adjacent vertex distinguishing total colorings of outerplanar graphs," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 123-133, February.
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    Cited by:

    1. Jingjing Huo & Yiqiao Wang & Weifan Wang & Wenjing Xia, 2020. "Neighbor-distinguishing total coloring of planar graphs with maximum degree twelve," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 246-272, January.

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