Hamilton decompositions of regular tournaments
arXiv:0908.3411 · doi:10.1112/plms/pdp062
Abstract
We show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each η>0 every regular tournament G of sufficiently large order n contains at least (1/2-η)n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968. Our result also extends to almost regular tournaments.
38 pages, 2 figures. Added section sketching how we can extend our main result. To appear in the Proceedings of the LMS