最大度不小于6的伪-Halin图的完备色数

On the Complete Chromatic Number of Pseudo-Halin Graphs with △(G)≥6

中文关键词:  伪-Halin图  Halin-图  完备色数

英文关键词:Pseudo-Halin graph  complete coloring  complete chromatic number.

中文摘要:

      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 X_C（C）=△（G）+1.其中△（G）和X_C（G）分别表示G的最大度和完备色数.

英文摘要:

      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 X_C(G) = △(G) + 1 . Where △(G) , X_C(G) denote the maximum degree and the complete chromatic number of G, respectively. V(f₀) denotes the vertices on the boundary of f₀.