Longest Cycles in 3-Connected, K_(1,3)-Free Graphs

The graph considered in this paper is an undireeted graph of order n,without loops alld multiple edges.Denotea by V(G)the vertex set of graph G,by |V(G)| the cardinality of V(G),by K(G)the connectivity of G,by δ the minimum degree of G.A eyele in G is considered as a Subgraph of G,and for a Subgraph H of G.1et G-H denote the Subgraph of G inducedby vertex set V(G)-y(日).M. M.Marthews and D.P.Summer proved in 1986 that eVery 2-eonneeted, K_1,3-free