Longest cycles in k-connected graphs with given independence number

The Chvátal–Erdős Theorem states that every graph whose connectivity is at least its independence number has a spanning cycle. In 1976, Fouquet and Jolivet conjectured an extension: If G is an n-vertex k-connected graph with independence number a, and a ⩾ k , then G has a cycle with length at least k ( n + a − k ) a . We prove this conjecture.