一类泛连通无爪图

A KIND OF PANCONNECTED K_(1,3)-FREE GRAPH

本文证明了如果Ｇ是３连通无爪图，且Ｇ的每个导出子图Ａ，Ａ＋都满足（ａ１，ａ２），则Ｇ是泛连通图（除了当ｕ，ｖ∈Ｖ（Ｇ），ｄ（ｕ，ｖ）＝１时，Ｇ中可能不存在（ｕ，ｖ）－ｋ路外，这里２≤ｋ≤４）．

This paper proves that: let G be a 3-connected K1,3-free graph; if every induced subgraph A or A+ of G satisfies (a1,a2), then G is panconnected (Except for that when u, v ∈ V(G), and d(u, v) = 1, there may not be (u, v)-k paths for k = 2, 3, 4).