Abstract
A graph G with vertex set V( G) and edge set E( G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V( G) |. Theorem. Let G be Hamiltonian and suppose that |E(G)| ≥ n 2 4 , where n = | V( G)|. Then G is either pancyclic or else is the complete bipartite graph K n 2 , n 2 . As a corollary to this theorem it is shown that the Ore conditions for a graph to be Hamiltonian actually imply that the graph is either pancyclic or else is K n 2 , n 2 .
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