Bondy and Chv\'atal theorem BondyAndChvatalTheorem 2001-10-24 13:42:07 2006-10-23 15:03:18 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} %\usepackage{graphicx} %\usepackage{xypic} \textbf{Bondy and Chv\'atal's theorem.}\\ Let $G$ be a graph of order $n\ge 3$ and suppose that $u$ and $v$ are distinct non adjacent vertices such that $\deg(u)+\deg(v)\ge n$. Then $G$ is Hamiltonian if and only if $G+uv$ is Hamiltonian.