Ore's theorem OresTheorem 2001-10-24 12:57:09 2006-09-20 00:50:23 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $G$ be a simple graph of order $n\ge 3$ such that, for every pair of distinct non adjacent vertices $u$ and $v$, $\deg(u)+\deg(v)\ge n$. Then $G$ is a Hamiltonian graph.