The Maximum Number of Cliques in Graphs with Bounded Odd Circumference

In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Turán-type result is an extension of the celebrated Erdős and Gallai theorem and a strengthening of Luo’s recent result. The same bound for graphs with bounded even circumferences is a trivial application of the theorem of Li and Ning.