Hamiltonian-Connected Graphs with Large Neighborhoods and Degrees

Abstract

For a simple graph $G$, let $C(G) = \min \{ \vert N(u) \cup N(v) \vert : u,v \in V(g), \ uv \notin E(G) \}$. In this paper we prove that if $NC(G) + \delta (G) \ge \vert V(G) \vert$, then either $G$ is Hamiltonian-connected, or $G$ belongs to a well-characterized class of graphs. The former result by Dirac, Ore and Faudree et al. are extended.