Complementary cycles of any length in regular bipartite tournaments

Stéphane Bessy, Jocelyn Thiebaut

Let $D$ be a $k$-regular bipartite tournament on $n$ vertices. We show that, for every $p$ with $2\le p\le n/2-2$, $D$ has a cycle $C$ of length $2p$ such that $D\setminus C$ is…