Pancyclicity of highly connected graphs

A well-known result due to Chvátal and Erdős (1972) asserts that, if a graph G satisfies κ(G) ≥ α(G) , where κ(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 κ(G) > α(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.