Let $\chi'_{a}(G)$ and Δ(G) denote the acyclic chromatic index and the maximum degree of a graph G, respectively. Fiamă?ik 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.
['Yingqian Wang', 'Ping Sheng']
Improved upper bound for acyclic chromatic index of planar graphs without 4-cycles