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Minimum total coloring of planar graphs with maximum degree 8

Author

Listed:
  • Liting Wang

    (Qingdao University)

  • Huijuan Wang

    (Qingdao University)

  • Weili Wu

    (University of Texas at Dallas)

Abstract

We define G to be a planar graph with maximum degree $$\varDelta $$ Δ . Suppose $$\varDelta \ge 8$$ Δ ≥ 8 and G has no adjacent p,q-cycles for some p, $$q\in \{3,4,5,6,7,8\}$$ q ∈ { 3 , 4 , 5 , 6 , 7 , 8 } , then G can be totally colored by $$(\varDelta +1)$$ ( Δ + 1 ) colors.

Suggested Citation

  • Liting Wang & Huijuan Wang & Weili Wu, 2023. "Minimum total coloring of planar graphs with maximum degree 8," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-11, March.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-01011-y
    DOI: 10.1007/s10878-023-01011-y
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    References listed on IDEAS

    as
    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. Huijuan Wang & Bin Liu & Yan Gu & Xin Zhang & Weili Wu & Hongwei Gao, 2017. "Total coloring of planar graphs without adjacent short cycles," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 265-274, January.
    3. Huijuan Wang & Bin Liu & Xiaoli Wang & Guangmo Tong & Weili Wu & Hongwei Gao, 2017. "Total coloring of planar graphs without adjacent chordal 6-cycles," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 257-265, July.
    Full references (including those not matched with items on IDEAS)

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