Completing the solution of the directed Oberwolfach problem with cycles of equal length

Abstract

In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of odd length. We prove that the complete symmetric digraph on $2m$ vertices, denoted $K_{2m}^{\ast }$, admits a resolvable decomposition into directed cycles of odd length $m$. This completely settles the directed Oberwolfach problem with tables of uniform length.

arXiv comment25 pages with 22 figures