科研之友
微信
新浪微博
Facebook
分享链接
摘要
A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by x' (a) (G), is the least number of colors such that G has an acyclic edge k-coloring. Let G be a graph with maximum degree Delta and girth g(G), and let 1 <= r <= 2 Delta be an integer. In this paper, it is shown that there exists a constant c > 0 such that if g(G) >= C Delta/r log(Delta(2)/r) then x' (a) (G) <= Delta+r + 1, which generalizes the result of Alon et al. in 2001. When G is restricted to series-parallel graphs, it is proved that x' (a) (G) = Delta if Delta >= 4 and g(G) >= 4; or Delta >= 3 and g(G) >= 5.
- 出版日期2012-12
- 单位福州大学
