Pancyclic graphs I


AbstractA 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)| ≥ n24, where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph Kn2,n2.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 Kn2, n2

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Last time updated on 6/5/2019

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