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

  • Authors:

  • Yingqian Wang;Ping Sheng

  • Affiliations:

  • Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004;Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

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Abstract

Let $\chi'_{a}(G)$ and Δ(G) denote the acyclic chromatic index and the maximum degree of a graph G, respectively. Fiamă驴ík 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.