最大度不小于5的外平面图的邻强边染色

图G(V,E)的一k-正常边染色叫做k-邻强边染色当且仅当对任意uv∈E(G)有,fu]≠fv],其中fu]={f(uw)|uw∈E(G)},f(uw)表示边uw的染色.并且x'as(G)=min{k|存在k-图G的邻强边染色}叫做图G的图的邻强边色数.本文证明了对最大度不小于5的外平面图有△≤x'as(G)≤△ 1,且x'as(G)=△ 1当且仅当存在相邻的最大度点.

On the Adjacent Strong Edge Coloring of Outer Plane Graphs

A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper kedge coloring f of graph G(V, E) such that fu] ≠ fv] for every uv ∈ E(G), where fu] ={f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x′as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △≤ x′as(G) ≤△ + 1 for outer plane graphs with △(G) ≥ 5, and x′as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree.