Abstract
A well-known result by O. Ore is that every graph of order n with d(u)+d(v)≥n+1 for any pair of nonadjacent vertices u and v is hamiltonian connected (i.e., for every pair of vertices, there is a hamiltonian path joining them). In this paper, we show that every 3-connected claw-free graph G on at most 5δ−8 vertices is hamiltonian connected, where δ denotes the minimum degree in G. This result generalizes several previous results.
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