Abstract
Let \(\chi'_{a}(G)\) and Δ(G) denote the acyclic chromatic index and the maximum degree of a graph G, respectively. Fiamčík conjectured that \(\chi'_{a}(G)\leq \varDelta (G)+2\). Even for planar graphs, this conjecture remains open with large gap. Let G be a planar graph without 4-cycles. Fiedorowicz et al. showed that \(\chi'_{a}(G)\leq \varDelta (G)+15\). Recently Hou et al. improved the upper bound to Δ(G)+4. In this paper, we further improve the upper bound to Δ(G)+3.
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Supported by the Natural Science Foundation of Zhejiang Province, China, Grant No. Y6090699, partially supported by the Natural Science Foundation of China, Grant No. 10971198, and Zhejiang Innovation Project, Grant No. T200905.
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Wang, Y., Sheng, P. Improved upper bound for acyclic chromatic index of planar graphs without 4-cycles. J Comb Optim 27, 519–529 (2014). https://doi.org/10.1007/s10878-012-9524-5
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DOI: https://doi.org/10.1007/s10878-012-9524-5