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

Ruiying Yang, Yuehua Bu, Junlei Zhu and Hongguo Zhu ()
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Ruiying Yang: Zhejiang Normal University
Yuehua Bu: Zhejiang Normal University
Junlei Zhu: Jiaxing University
Hongguo Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 54, 13 pages

Abstract: 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 .

Keywords: r-Dynamic coloring; Planar graphs; Cycle; Discharging; 05C10; 05C15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00985-5

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