or v is at least 2n − 1 must be Hamiltonian. Ore's theorem may also be strengthened to give a stronger conclusion than Hamiltonicity as a consequence of the degree condition in the theorem. Specifically, every graph satisfying the conditions of Ore's theorem is either a regular complete bipartite graph or is pancyclic . References . . . . . Extremal graph theory Theorems in graph theory Articles containing proofs Hamiltonian paths and cycles