Sufficient conditions for graphs to be spanning connected

Abstract A graph G is t*-connected if there exist t internally disjoint (u, v)-paths, between any two vertices u and v, whose union spans G. In this sense, t*-connectedness is a natural extension of hamiltonicity. In this paper, we provide a sufficient condition for graphs to be t*-connected by generalizing a classic result given by Chavatal [7]. Furthermore, as byproducts, we extend some known results concerning fault tolerant hamiltonicity and minimum cardinality of edges. We also establish analogous results for balanced bipartite graphs.