Abstract
A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G. The acyclic edge chromatic number of G, denoted byχ′ a (G), is the smallest number of colors in an acyclic edge coloring of G. Let G be a planar graph with maximum degree Δ. In this paper, we show that χ′ a (G) ⩽ Δ + 2, if G has no adjacent i- and j-cycles for any i, j ∈ {3, 4, 5}, which implies a result of Hou, Liu and Wu (2012); and χ′ a (G) ⩽ Δ + 3, if G has no adjacent i- and j-cycles for any i, j ∈ {3, 4, 6}.
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Wan, M., Xu, B. Acyclic edge coloring of planar graphs without adjacent cycles. Sci. China Math. 57, 433–442 (2014). https://doi.org/10.1007/s11425-013-4644-7
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DOI: https://doi.org/10.1007/s11425-013-4644-7