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The r-dynamic chromatic number of planar graphs without 4-,5-cycles

Author

Listed:
  • Ruiying Yang

    (Zhejiang Normal University)

  • Yuehua Bu

    (Zhejiang Normal University
    Zhejiang Guangsha Vocational and Technical University of Construction)

  • Junlei Zhu

    (Jiaxing University)

  • Hongguo Zhu

    (Zhejiang Normal University)

Abstract

Let G be a graph and k, r be two positive integers. A (k, r)-dynamic coloring $$\varphi $$ φ of G is a proper k-coloring such that $$\mid \varphi (N_{G}(v))\mid \ge $$ ∣ φ ( N G ( v ) ) ∣ ≥ $$\min \{d_{G}(v),r\}$$ min { d G ( v ) , r } for each $$v\in V(G)$$ v ∈ V ( G ) . In this paper, we prove that the r-dynamic chromatic number of planar graphs without 4-,5-cycles, and intersecting 3-cycles is at most $$r+3$$ r + 3 if $$r\ge 14$$ r ≥ 14 .

Suggested Citation

  • Ruiying Yang & Yuehua Bu & Junlei Zhu & Hongguo Zhu, 2023. "The r-dynamic chromatic number of planar graphs without 4-,5-cycles," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-13, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00985-5
    DOI: 10.1007/s10878-022-00985-5
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    References listed on IDEAS

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    1. Junlei Zhu & Yuehua Bu, 2018. "Minimum 2-distance coloring of planar graphs and channel assignment," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 55-64, July.
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