2012/03/23 by Yue Guan, Jianfeng Hou, Guan, Yue +3
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1203.5186
arxiv created 2012/03/23 · arxiv updated 2012/03/26
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 edge-coloring of planar graphs, SIAM J. Discrete Math. 25 (2) (2011), 463--478] showed that χ'a(G)≤ Δ(G)+12 for planar graphs G with maximum degree Δ(G). In this paper, the bound is improved to Δ(G)+10.