# Bondy and Chvátal theorem

Bondy and Chvátal’s theorem.
Let $G$ be a graph of order $n\geq 3$ and suppose that $u$ and $v$ are distinct non adjacent vertices such that $\deg(u)+\deg(v)\geq n$.

Then $G$ is Hamiltonian if and only if $G+uv$ is Hamiltonian.

 Title Bondy and Chvátal theorem Canonical name BondyAndChvatalTheorem Date of creation 2013-03-22 11:52:57 Last modified on 2013-03-22 11:52:57 Owner drini (3) Last modified by drini (3) Numerical id 9 Author drini (3) Entry type Theorem Classification msc 05C45 Classification msc 81P99 Classification msc 81S30 Classification msc 81S99 Classification msc 81-00 Classification msc 81S05 Classification msc 81P15 Related topic HamiltonianGraph Related topic OresTheorem