The maximum number of cliques in graphs with bounded odd circumference

TL;DR

This paper establishes the maximum number of cliques in graphs with bounded odd circumference, extending classical theorems and providing a sharp upper bound for such graphs.

Contribution

It generalizes Turán-type results to graphs with bounded odd circumferences, extending Erdős-Gallai and Luo's results.

Findings

Sharp upper bound for cliques in graphs with bounded odd circumference

Extension of Erdős-Gallai theorem to odd circumferences

Strengthening of Luo's recent results

Abstract

In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Tur\'an-type result is an extension of the celebrated Erd\H{o}s 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.