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Strong Edge Coloring of Subquartic Graphs

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14462))

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Abstract

A strong k-edge coloring of a graph G is a mapping \(c: E(G)\rightarrow \{1,2,3,...,k\}\) such that for any two edges e and \(e'\) with distance at most two, \(c(e)\ne c(e')\). The strong chromatic index of G, written \(\chi '_s(G)\), is the smallest integer k such that G has a strong k-edge coloring. In this paper, using color exchange method and discharging method, we prove that for a subquartic graph G, \(\chi _s'(G)\le 11\) if \(mad(G)<\frac{8}{3}\), where \(mad(G)=\max \{\frac{2|E(G)|}{|V(G)|},H\subseteq G\}\).

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Acknowledgement

This research was supported by National Natural Science Foundation of China under Grant Nos. 11901243, 12201569 and Qin Shen Program of Jiaxing University.

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Authors and Affiliations

  1. College of Data Science, Jiaxing University, Jiaxing, 314001, China

    Junlei Zhu

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Hongguo Zhu

Authors
  1. Junlei Zhu
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  2. Hongguo Zhu
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Correspondence to Junlei Zhu .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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We declare that we have no conflicts of interest to this work. We also declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Zhu, J., Zhu, H. (2024). Strong Edge Coloring of Subquartic Graphs. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14462. Springer, Cham. https://doi.org/10.1007/978-3-031-49614-1_9

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  • DOI: https://doi.org/10.1007/978-3-031-49614-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49613-4

  • Online ISBN: 978-3-031-49614-1

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