Approximate Jackson conjecture for regular bipartite digraphs

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 set into Hamilton cycles. Approximate Jackson conjecture. Let $c>1/2$ and let $n$ be sufficiently large. Then every $cn$-regular bipartite digraph $G$ on $2n$ vertices has a Hamilton cycle decomposition. The paper proves an almost decomposition leaving an arbitrarily small proportion of the edges uncovered, while the exact decomposition remains open.