三角连通(K_(1,4);2)-图的完全圈可扩性

Fully Circle Extendability of Triangularly Connected (K_(1,4);2)-Graphs

对于任意一对边e1,e2∈E(G),在G中存在一系列3-圈C1,C2…,Cl使得e1∈C1,e2∈Cl且E(Ci)∩E(Ci+1)≠Φ(1≤i≤l-1),则称图G为三角连通的.本文证明如下结论:顶点数不小于3,无孤立点,爪心独立的三角连通(K1,4;2)-图是完全圈可扩的.

A graph G is triangularly connected if for every pair of edges e1, e2 ∈ E （G）, G has a sequence of 3-cycles C1, C2,…, Ct, which meet the condition of e1 ∈ C1, e2 ∈ Cl and E（Ci） ∩ E （ Ci ＋ 1 ） ≠ Ф （ 1 ≤ i ≤ l - 1 ）. This paper proves that every triangularly connected （ K1,4 ; 2）-graph with independent claw centers and at least three vertices and without any isolated vertex is full circle and extendable.