A theorem on even pancyclic bipartite digraphs

Abstract

We prove that a strongly connected balanced bipartite directed graph of order $2a\ge 6$ with partite sets $X$ and $Y$ contains cycles of every length $2,4,\dots ,2a$, provided $d(x)+d(y)\ge 3a$ for every pair of vertices $x$, $y$ either both in $X$ or both in $Y$.

12 pages