Geodesic
A note on a new condition implying pancyclism
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 137-143.

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We first show that if a 2-connected graph G of order n is such that for each two vertices u and v such that δ = d(u) and d(v) n/2 the edge uv belongs to E(G), then G is hamiltonian. Next, by using this result, we prove that a graph G satysfying the above condition is either pancyclic or isomorphic to K_n/2,n/2.
Keywords: hamiltonian graphs, pancyclic graphs, cycles 
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Flandrin, Evelyne; Li, Hao; Marczyk, Antoni; Woźniak, Mariusz. A note on a new condition implying pancyclism. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 137-143. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a9/

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