Improved upper bound for acyclic chromatic index of planar graphs without 4-cycles

Yingqian Wang () and Ping Sheng
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Yingqian Wang: Zhejiang Normal University
Ping Sheng: Zhejiang Normal University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 3, No 7, 519-529

Abstract: 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.

Keywords: Planar graph; Acyclic edge coloring; 4-Cycles (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9524-5

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