Ore's Theorem

Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph with "sufficiently many edges" must contain a Hamilton cycle. Specifically, the theorem considers the sum of the degrees of any two non-adjacent vertices: if this sum is always at least equal to the total number of vertices in the graph, then the graph is Hamiltonian.