  A well-known result due to Chvat\'al and Erd\H{o}s (1972) asserts that, if a
graph $G$ satisfies $\kappa(G) \ge \alpha(G)$, where $\kappa(G)$ is the
vertex-connectivity of $G$, then $G$ has a Hamilton cycle. We prove a similar
result implying that a graph $G$ is pancyclic, namely it contains cycles of all
lengths between $3$ and $|G|$: if $|G|$ is large and $\kappa(G) > \alpha(G)$,
then $G$ is pancyclic. This confirms a conjecture of Jackson and Ordaz (1990)
for large graphs, and improves upon a very recent result of Dragani\'c,
Munh\'a-Correia, and Sudakov.
