An application of the solution of Kirkman's schoolgirl problem: The decomposition of the symmetric oriented complete graph into 3-circuits

Abstract

In this paper, we show that if K n ∗ denotes the symmetric oriented complete graph on n vertices, with n ≠ 6, then we can partition the arcs of K n ∗ into oriented 3-circuits if and only if n( n−1) ≡ 0 (mod 3). We use the solution of Kirkman's schoolgirl problem given by Ray-Chaudhuri and Wilson [1].