An improved bound on acyclic chromatic index of planar graphs

Abstract

A proper edge coloring of a graph G is called acyclic if there is no bichromatic cycle in G. The acyclic chromatic index of G, denoted by χ ′ a (G), is the least number of colors k such that G has an acyclic edge k-coloring. Basavaraju et al. [Acyclic edgecoloring of planar graphs, SIAM J. Discrete Math. 25 (2) (2011), [463][464][465][466][467][468][469][470][471][472][473][474][475][476][477][478] showed that χ ′ a (G) ≤ ∆(G) + 12 for planar graphs G with maximum degree ∆(G). In this paper, the bound is improved to ∆(G) + 10.