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 pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.

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