摘要
设G为2-连通平面图,若存在G的面f0,其中f0的边界构成的圈上无弦且V（f0）中的点的度至少为3,使得在G中去掉f0边界上的所有边后得到的图为除V（f0）中的点外度不小于3的树T,则称G为伪-Halin图;若V（f0）中的点全为3度点,则称G为Halin-图.本文研究了这类图的完备色数,并证明了对△（G）≥ 6的伪-Halin图 G有 Xc（C）=△（G）+1.其中△（G）和Xc（G）分别表示G的最大度和完备色数.
Let G(V,E) be a 2-connected plane graph, f0 a face without chord on its boundary (a cycle) and d(.v)≥ 3 for every v ∈ V(f0) . If the graph T obtained from G(V,E) by deleting all edges on the boundary of f0 is a tree of which all vertices v ∈ V\V(f0) satisfy d(.v)≥ 3 , then G(V,E) is called a Pseudo-Halin graph; G(V,E) is said to be Halin-graph iif d(v) = 3 for every v ∈ V(f0) . In this paper,we proved that for any Pseudo-Halin graph with △(G) ≥ 6 , have XC(G) = △(G) + 1 . Where △(G) , Xc(G) denote the maximum degree and the complete chromatic number of G , respectively. V(f0) denotes the vertices on the boundary of f0.
基金
国家自然科学基金资助项目(19871036)
