Hamilton-Connectivity of k1,3-Free Graphs

Abstract:

      In this paper, we proved the following result: Let G be a simple 3-connec-ted k_1,3- free graph of order p. If for any independent sets {x₁,x₂,x₃} of three vertices in G, we haved(x₁)+d(x₂)+d(x₃)≥p+1.Then G is Hamilton connected.