Hamilton decompositions of regular bipartite tournaments

TL;DR

This paper proves Jackson's conjecture that all sufficiently large regular bipartite tournaments can be decomposed into Hamilton cycles, and also confirms a related conjecture on dense bipartite digraphs.

Contribution

It establishes the Hamilton decomposition for large regular bipartite tournaments and proves a conjecture on Hamilton decompositions of dense bipartite digraphs.

Findings

Proved Jackson's conjecture for large bipartite tournaments.

Confirmed a conjecture on Hamilton decompositions of dense bipartite digraphs.

Extended understanding of Hamilton cycle decompositions in bipartite graphs.

Abstract

A regular bipartite tournament is an orientation of a complete balanced bipartite graph $K_{2n,2n}$ where every vertex has its in- and outdegree both equal to $n$. In 1981, Jackson conjectured that any regular bipartite tournament can be decomposed into Hamilton cycles. We prove this conjecture for all sufficiently large bipartite tournaments. Along the way, we also prove several further results, including a conjecture of Liebenau and Pehova on Hamilton decompositions of dense bipartite digraphs.