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List edge and list total coloring of planar graphs with maximum degree 8

Author

Listed:
  • Huijuan Wang

    (Qingdao University)

  • Bin Liu

    (Ocean University of China)

  • Xin Zhang

    (Xidian University)

  • Lidong Wu

    (University of Texas at Tyler)

  • Weili Wu

    (TaiYuan University of Technology
    University of Texas at Dallas)

  • Hongwei Gao

    (Qingdao University)

Abstract

Let $$G$$ G be a planar graph with maximum degree $$\varDelta \ge 8$$ Δ ≥ 8 and without chordal 5-cycles. Then $$\chi '_{l}(G)=\varDelta $$ χ l ′ ( G ) = Δ and $$\chi ''_{l}(G)=\varDelta +1$$ χ l ′ ′ ( G ) = Δ + 1 .

Suggested Citation

  • Huijuan Wang & Bin Liu & Xin Zhang & Lidong Wu & Weili Wu & Hongwei Gao, 2016. "List edge and list total coloring of planar graphs with maximum degree 8," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 188-197, July.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:1:d:10.1007_s10878-015-9870-1
    DOI: 10.1007/s10878-015-9870-1
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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. Huijuan Wang & Lidong Wu & Weili Wu & Jianliang Wu, 2014. "Minimum number of disjoint linear forests covering a planar graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 274-287, July.
    3. Huijuan Wang & Lidong Wu & Weili Wu & Panos Pardalos & Jianliang Wu, 2014. "Minimum total coloring of planar graph," Journal of Global Optimization, Springer, vol. 60(4), pages 777-791, December.
    4. Patrizio Angelini & Fabrizio Frati, 2012. "Acyclically 3-colorable planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 116-130, August.
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    Cited by:

    1. Qiufen Ni & Smita Ghosh & Chuanhe Huang & Weili Wu & Rong Jin, 2021. "Discount allocation for cost minimization in online social networks," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 213-233, January.
    2. Cai, Jiansheng & Li, Wenwen & Cai, Wenjing & Dehmer, Matthias, 2023. "List injective coloring of planar graphs," Applied Mathematics and Computation, Elsevier, vol. 439(C).

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