Packings of the complete directed graph with \(m\)-circuits (Q1288226)

Let \(\text{DK}_v\) denote the complete directed symmetric graph with \(v\) vertices. A packing of \(\text{DK}_v\) with \(m\)-circuits is defined to be a family of arc-disjoint \(m\)-circuits of \(\text{DK}_v\) such that any arc of \(\text{DK}_v\) occurs in at most one \(m\)-circuit. The packing number \(P(v,m)\) is the maximum number of \(m\)-circuits in such a packing. The authors continue the study of this problem and prove the following results: (1) The values of \(P(v,m)\) are completely determined for \(m= 12,14\), and 16. (2) The problem is reduced to the case \(m+6\leq v\leq 2m-\lfloor (\sqrt{4m- 3}+1)/2\rfloor\) for any fixed even integer \(m\geq 4\).