摘要
图G的C 划分是指 :G的一个顶点划分 {V1 ,V2 ,… ,Vk}使得每个G[Vi]为多重完全图 (1≤i≤k) .证明了如下结果 :设G为连通图 ,且对任意v∈V(G) ,dG(v)≡ 1 (mod 4) .若G的顶点集存在一个C 划分 {V1 ,V2 ,… ,Vk}使得对每个 1≤i≤k,|Vi|≥ 4 ,且 |Vi|≡ 0 (mod 4) ,则G是上可嵌入的 .另外 ,联系着图的点的度和其它条件 ,推广和深化了目前有关这方面的一些结果 。
Let G be a graph, if there exists a partition | V1, V2, ···, V4 | of V(G) satisfying G[V1] a multiple complete graph for any i ∉ [ 1,k ], then G has a C-partition. The authors state such a result: Let G be a connected graph, and dc (v) = 1 (mod 4) for any v∉ V(G), if the vertex-set of G has a C-partition | V1, V2, ···, V4 | satisfying | Vi | ≥4 and | Vi | = 0(mod 4) for any i ∉ [ 1, k], then G is upper-embeddable. In addition, connected with the degree of a vertex in a graph and the other conditions, we widen and deepens some result about the article and then gives some other upper-embeddable graphs.
出处
《晓庄学院自然科学学报》
EI
CAS
北大核心
2002年第3期1-4,共4页
Journal of Natural Science of Hunan Normal University
基金
国家自然科学基金资助项目(1 980 1 0 1 3)
