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Injective edge-coloring of claw-free subcubic graphs

Author

Listed:
  • Qing Cui

    (Nanjing University of Aeronautics and Astronautics)

  • Zhenmeng Han

    (Nanjing University of Aeronautics and Astronautics)

Abstract

An injective edge-coloring of a graph G is an edge-coloring of G such that any two edges that are at distance 2 or in a common triangle receive distinct colors. The injective chromatic index of G is the minimum number of colors needed to guarantee that G admits an injective edge-coloring. Ferdjallah, Kerdjoudj and Raspaud showed that the injective chromatic index of every subcubic graph is at most 8, and conjectured that 8 can be improved to 6. Kostochka, Raspaud and Xu further proved that every subcubic graph has the injective chromatic index at most 7, and every subcubic planar graph has the injective chromatic index at most 6. In this paper, we consider the injective edge-coloring of claw-free subcubic graphs. We show that every connected claw-free subcubic graph, apart from two exceptions, has the injective chromatic index at most 5. We also consider the list version of injective edge-coloring and prove that the list injective chromatic index of every claw-free subcubic graph is at most 6. Both results are sharp and strengthen a recent result of Yang and Wu which asserts that every claw-free subcubic graph has the injective chromatic index at most 6.

Suggested Citation

  • Qing Cui & Zhenmeng Han, 2024. "Injective edge-coloring of claw-free subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-32, July.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:5:d:10.1007_s10878-024-01188-w
    DOI: 10.1007/s10878-024-01188-w
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    References listed on IDEAS

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    1. Min Chen & Geňa Hahn & André Raspaud & Weifan Wang, 2012. "Some results on the injective chromatic number of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 299-318, October.
    2. Qiming Fang & Li Zhang, 2022. "Sharp upper bound of injective coloring of planar graphs with girth at least 5," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1161-1198, September.
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