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On Strong Edge-Coloring of Claw-Free Subcubic Graphs

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Abstract

A strong edge-coloring of a graph G is a proper edge coloring such that every path of length 3 uses three different colors. The strong chromatic index of G, denoted by \(\chi _{s}^{\prime }(G)\), is the least possible number of colors in a strong edge-coloring of G. In this paper, we prove that if G is a claw-free subcubic graph other than the prism graph, then \(\chi _{s}^{\prime }(G)\le 8\).

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Acknowledgements

Supported by the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics.

Funding

Research of Jian-Bo Lv was supported by NSFC (No.12161010) and Youth Science Foundation of Guangxi (No.2019JJB110007). Research of Jianxi Li was supported by NSF of China (No.12171089) and NSF of Fujian (No.2021J02048). Research of Xiaoxia Zhang was supported by NSF of China (No.11701496).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541000, People’s Republic of China

    Jian-Bo Lv

  2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, People’s Republic of China

    Jianxi Li

  3. Department of Mathematics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China

    Xiaoxia Zhang

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  1. Jian-Bo Lv
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  2. Jianxi Li
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Correspondence to Jianxi Li.

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Research of Jian-Bo Lv was supported by NSFC (No.12161010) and Youth Science Foundation of Guangxi (No.2019JJB110007). Research of Jianxi Li was supported by NSF of China (No.12171089) and NSF of Fujian (No.2021J02048). Research of Xiaoxia Zhang was supported by NSF of China (No.11701496).

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Lv, JB., Li, J. & Zhang, X. On Strong Edge-Coloring of Claw-Free Subcubic Graphs. Graphs and Combinatorics 38, 63 (2022). https://doi.org/10.1007/s00373-022-02462-6

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  • DOI: https://doi.org/10.1007/s00373-022-02462-6

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