Fan 型条件与泛连通性

设G是n(≥5)个顶点的简单图.本文证明了若对G的任意一对距离为2的顶点u,v都有max{d(u),d(v)}≥(n+1)/2成立,则G中任一对顶点x和y之间存在长为6到n-1的路.，Let G be a simple graph with n(≥5) vertices. In this paper, we prove that if G is 3-connected and satisfies that d(u,v)=2 implies max {d(u),d(v)}≥(n+1) /2 for every pair of vertices u and v in G, then for any two vertices x, y of G, there are (x,y)-paths of length from 6 to n-1 in G, and there are (x,y)-paths of length from 5 to n-1 in G unless G[(N)(x)]=G[(N)(y)]≌K4or K5, or G[(N)(x)],G[(N)(y)]are complete and (N)(x)(n)(N)(y)=φ.

Fan-Type Condition and Panconnectivity