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 \(\varDelta \) is acyclically edge-\((\varDelta +2)\)-colorable. Basavaraju and Chandran (J Graph Theory 61:192–209, 2009) confirmed the conjecture for non-regular graphs G with \(\varDelta =4\). In this paper, we extend this result by showing that every 4-regular graph G without 3-cycles is acyclically edge-6-colorable.
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Qiaojun Shu research was supported partially by ZJNSF (LQ15A010010) and NSFC (No. 11601111). Yiqiao Wang research was supported partially by NSFC (Nos. 11301035 and 11671053); Weifan Wang research was supported partially by NSFC (Nos. 11071223 and 11371328).
Communicated by Xueliang Li.
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Shu, Q., Wang, Y., Ma, Y. et al. Acyclic Edge Coloring of 4-Regular Graphs Without 3-Cycles. Bull. Malays. Math. Sci. Soc. 42, 285–296 (2019). https://doi.org/10.1007/s40840-017-0484-x
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DOI: https://doi.org/10.1007/s40840-017-0484-x