无爪图中不相邻子图P_4和K_1度和条件下的哈密尔顿连通性

The Hamilton-connectivity with the degree sum of non-adjacent subgraphs P_4 and K_1 in claw-free graphs

研究子图的度和图的哈密尔顿性的关系,证明图G是一个n阶3-连通无爪图且最小度δ(G)≥4,如果图G中任意两个分别同构于P_4,K_1的不相邻子图H_1,H_2满足d(H_1)+d(H_2)≥n,则图G是哈密尔顿连通.

This paper studies the relationship between the degree of subgraphs and Hamiltonicity of graphs.It is proven that every 3-connected claw-free graph G of order n with minimum degree δ（G）≥4 is Hamilton-connected if it satisfies d（H1）＋d（H2）≥n for any two non-adjacent subgraphs H_1,H_2 which are isomorphic to P4,K1 respectively.