Turan-type problem for a cycle of length 6 in bipartite Eulerian digraph

@article{Goya2016TurantypePF,
  title={Turan-type problem for a cycle of length 6 in bipartite Eulerian digraph},
  author={Hideki Goya},
  journal={Ars Comb.},
  year={2016},
  volume={128},
  pages={255-262}
}
We prove the following Turán-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.