Turán-Type Problem for a Cycle of Length \(6\) in Bipartite Eulerian Digraph

Abstract

We prove the following Turdn-Type result: If there are more than \(9mn/16\) edges in a simple and bipartite Eulerian digraph with vertex partition size m and n, then the graph contains a directed cycle of length \(4\) or \(6\). By using this result, we improve an upper bound for the diameter of interchange graphs.