A note on a new condition implying pancyclism
Evelyne Flandrin, Hao Li, Antoni Marczyk, Mariusz Woźniak · Discussiones Mathematicae Graph Theory · 2001
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 ‐ = 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 Kn=2;n=2.