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Acyclic Edge Coloring of Chordal Graphs with Bounded Degree

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Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. It was conjectured that every simple graph G with maximum degree \(\Delta \) is acyclically edge-\((\Delta +2)\)-colorable. In this paper, we confirm the conjecture for chordal graphs G with \(\Delta \le 6\).

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Acknowledgements

The first two authors were partially supported by the National Natural Science Foundation of China (No. 11922112), the Natural Science Foundation of Tianjin (Nos. 20JCJQJC00090 and 20JCZDJC00840) and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63213037). The third author was partially supported by NSFC (No. 11771402; No. 12031018).

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Authors and Affiliations

  1. Center for Combinatorics and LPMC, Nankai University, Tianjin, 300071, China

    Yulai Ma & Yongtang Shi

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

    Weifan Wang

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  1. Yulai Ma
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  2. Yongtang Shi
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  3. Weifan Wang
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Correspondence to Weifan Wang.

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Ma, Y., Shi, Y. & Wang, W. Acyclic Edge Coloring of Chordal Graphs with Bounded Degree. Graphs and Combinatorics 37, 2621–2636 (2021). https://doi.org/10.1007/s00373-021-02378-7

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  • DOI: https://doi.org/10.1007/s00373-021-02378-7

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