关于图的上可嵌入性的一个新的邻域条件

For A New Neighbor Condition on Up-Embeddabilitv of Graphs

用NG(u)表示一个图G中任意点u的邻域集. 其中K1,3,K1,3+e是G的点导出子图.本文主要证明了下述结果:设G是简单图,对L中任意两个距离为2的点u和v,即dL(u,v)=2,都有|NG(u)∩NG(v)|(?)2,则G是上可嵌入的.特别地,每个L-free图是上可嵌入的.

Let NG(u) denote the neighbor set of a vertex u in K1,3,K1,3+ e is the vertices induced subgraph of G.This paper mainly prove the following result:let G be a simple graph,for any two vertices u and v of diameter 2 in L,i.e., dL(u, v) = 2,satisfiy the condition 2,then G is up-embeddable.Especially, The L - free graphs are up-embeddable.