  A graph G is k-critical if every proper subgraph of G is (k-1)-colorable, but
the graph G itself is not. We prove that every k-critical graph on n vertices
has a cycle of length at least log n/(100log k), improving a bound of Alon,
Krivelevich and Seymour from 2000. Examples of Gallai from 1963 show that the
bound cannot be improved to exceed 2(k-1)log n/log(k-2). We thus settle the
problem of bounding the minimal circumference of k-critical graphs, raised by
Dirac in 1952 and Kelly and Kelly in 1954.
