摘要
双外平面图是一个平面图,它可以嵌入到平面上并使得它的顶点出现在两个面的边界上.设G是一个双外平面图,V(G)、E(G)、F(G)分别为双外平面图G的点集、边集和面集.G的全色数XT(G)是使得V(G)∪E(G)中的任意相邻或相关联的两个元素均染不同颜色的最少颜色数.本文证明了最大度至少是6的2连通的特殊双外平面图G的全色数是△(G)+1,其中△(G)为G的最大度数.
Let G be a special double-outer planar graph, V(G), E(G), F(G) be the set of vertices, edges and faces of G, respectively. A planar graph G is k-total colorable, if the elements of V(G)∪E(G) can be colored with k colors such that any two distinct adjacent or incident elements receive different colors. The total chromatic number, denoted by X_T(G), is defined as the minimum number k for which G is k-total colorable. We proved that if G is a special double-outer planar graph and Δ(G)≥6, then X_T(G)=Δ(G)+1.
出处
《洛阳大学学报》
2005年第2期7-9,共3页
Journal of Luoyang University
关键词
特殊双外平面图
全染色
全色数
a special double-outerplanar graphs
total coloring
total chromatic number
