4 problems

Let $n$ be the order of a bipartite biconnected digraph, let $r=\operatorname{rad}^+\geq 4$, and let $D_{n,r,s}$ be the specified digraph family. Let…

Let $G$ be a diregular bipartite tournament on $2n$ vertices, so $G$ is a complete bipartite orientation with equal indegree and outdegree at every vertex. Edge-disjoint Hamilton c…

Let $G$ be a $cn$-regular bipartite digraph on $2n$ vertices, meaning that every vertex has indegree and outdegree $cn$. A Hamilton cycle decomposition is a partition of the edge s…

Maximum-cycle degree conjecture. If this inequality holds whenever $u$ and $v$ lie in opposite colour classes and $uv\notin A(D)$, then $D$ contains an oriented cycle of length…