A well-known result due to Chvátal and Erdős (1972) asserts that, if a graph G satisfies (G) (G), where (G) is the vertex-connectivity of G, then G has a Hamilton cycle. We prove a similar result implying that a graph G is pancyclic, that is, it contains cycles of all lengths between 3 and |G|: if |G| is large and (G) > (G), then G is pancyclic. This confirms a conjecture of Jackson and Ordaz (1990) for large graphs, and improves upon a very recent result of Draganić, Munhá Correia, and Sudakov.
Shoham Letzter (Tue,) studied this question.