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A sufficient condition for planar graphs with girth 5 to be (1,6)-colorable

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  • Zhang, Ganchao
  • Chen, Min
  • Wang, Weifan

Abstract

A graph G is (d1,d2)-colorable if its vertices can be partitioned into two subsets V1 and V2 such that Δ(G[V1])≤d1 and Δ(G[V2])≤d2. Let G5 denote the family of planar graphs with girth at least 5. In this paper, we prove that every graph in G5 without adjacent 5-cycles is (1,6)-colorable.

Suggested Citation

  • Zhang, Ganchao & Chen, Min & Wang, Weifan, 2024. "A sufficient condition for planar graphs with girth 5 to be (1,6)-colorable," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001784
    DOI: 10.1016/j.amc.2024.128706
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    References listed on IDEAS

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    1. Wang, Yang & Huang, Danjun & Finbow, Stephen, 2020. "On the vertex partition of planar graphs into forests with bounded degree," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    2. Miao Zhang & Min Chen & Yiqiao Wang, 2017. "A sufficient condition for planar graphs with girth 5 to be (1, 7)-colorable," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 847-865, April.
    3. Lingji Xu & Zhengke Miao & Yingqian Wang, 2014. "Every planar graph with cycles of length neither 4 nor 5 is $$(1,1,0)$$ -colorable," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 774-786, November.
    4. Tingting Wu & Jiangxu Kong & Weifan Wang, 2016. "The 2-surviving rate of planar graphs without 5-cycles," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1479-1492, May.
    Full references (including those not matched with items on IDEAS)

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