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.
Citation
Zhao Kewen. Hong-Jian Lai. Ju Zhou. "Hamiltonian-Connected Graphs with Large Neighborhoods and Degrees." Missouri J. Math. Sci. 24 (1) 54 - 66, May 2012. https://doi.org/10.35834/mjms/1337950499
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