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2025, Volume 10, Issue 1: 1814-1825. doi: 10.3934/math.2025083
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On the list injective coloring of planar graphs without a 4−-cycle intersecting with a 5−-cycle

  • 1.
    Department of Mathematics, Zhejiang Normal University, Zhejiang, China
  • 2.
    Department of Basics, Zhejiang Guangsha Vocational and Technical University of Construction, Zhejiang, China
  • Received: 11 November 2024 Revised: 28 December 2024 Accepted: 17 January 2025 Published: 24 January 2025

  • MSC : 05C10, 05C15

  • An injective coloring of a graph G is a vertex coloring such that a pair of vertices obtain distinct colors if there is a path of length two between them. It is proved in this paper that χli(G)≤Δ+4 if Δ≥12 when G does not have a 4−-cycle intersecting with a 5−-cycle. Our result improves a previous result of Cai et al. in 2023, who showed that χli(G)≤Δ+4 when Δ≥12 and G has disjoint 5−-cycles.

    Citation: Yuehua Bu, Hongrui Zheng, Hongguo Zhu. On the list injective coloring of planar graphs without a 4−-cycle intersecting with a 5−-cycle[J]. AIMS Mathematics, 2025, 10(1): 1814-1825. doi: 10.3934/math.2025083

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  • An injective coloring of a graph G is a vertex coloring such that a pair of vertices obtain distinct colors if there is a path of length two between them. It is proved in this paper that χli(G)≤Δ+4 if Δ≥12 when G does not have a 4−-cycle intersecting with a 5−-cycle. Our result improves a previous result of Cai et al. in 2023, who showed that χli(G)≤Δ+4 when Δ≥12 and G has disjoint 5−-cycles.





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