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Acyclic Edge Coloring of 4-Regular Graphs (II)

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Abstract

A proper edge coloring is called acyclic if 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, combining some known results, we confirm the conjecture for graphs with \(\Delta =4\).

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Authors and Affiliations

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

    Weifan Wang & Yulai Ma

  2. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Qiaojun Shu

  3. School of Management, Beijing University of Chinese Medicine, Beijing, 100029, China

    Yiqiao Wang

Authors
  1. Weifan Wang
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  2. Yulai Ma
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  3. Qiaojun Shu
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  4. Yiqiao Wang
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Corresponding author

Correspondence to Yiqiao Wang.

Additional information

Communicated by Sanming Zhou.

Weifan Wang: Research supported partially by NSFC (Nos.11771402 and 11371328). Qiaojun Shu: Research supported partially by NSFC (No. 11601111) and ZJNSF (No. LQ15A010010). Yiqiao Wang: Research supported partially by NSFC (Nos. 11301035 and 11671053).

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Wang, W., Ma, Y., Shu, Q. et al. Acyclic Edge Coloring of 4-Regular Graphs (II). Bull. Malays. Math. Sci. Soc. 42, 2047–2054 (2019). https://doi.org/10.1007/s40840-017-0592-7

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  • DOI: https://doi.org/10.1007/s40840-017-0592-7

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