Ore's Theorem is a significant result in graph theory that provides a criterion for the existence of Hamiltonian cycles in a graph. Specifically, it states that if a graph has 'n' vertices (with n ≥ 3) and every pair of non-adjacent vertices has a combined degree of at least 'n', then the graph contains a Hamiltonian cycle. This theorem connects with the properties of both Eulerian and Hamiltonian paths and cycles by addressing conditions under which these cycles can be found.
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