Treedepth Versus Circumference

The circumference of a graph G is the length of a longest cycle in G, or +8 if G has no cycle. Birmele (J Graph Theory 43(1):24-25, 2003) showed that the treewidth of a graph G is at most its circumference minus 1. We strengthen this result for 2-connected graphs as follows: If G is 2-connected, then its treedepth is at most its circumference. The bound is best possible and improves on an earlier quadratic upper bound due to Marshall and Wood (J Graph Theory 79(3):222-232, 2015).