Pósa's theorem, in graph theory, is a sufficient condition for the existence of a Hamiltonian cycle based on the degrees of the vertices in an undirected graph.
Unlike those conditions, it can be applied to graphs with a small number of low-degree vertices.
It is named after Lajos Pósa, a protégé of Paul Erdős born in 1947, who discovered this theorem in 1962.
The Pósa condition for a finite undirected graph
Pósa's theorem states that if a finite undirected graph satisfies the Pósa condition, then that graph has a Hamiltonian cycle in it.