Optimal packing of even circuits into a \(\text{DK}_ v\) (Q1918209)

A packing of \(m\)-circuits into a complete directed symmetric graph with \(v\) vertices \((\text{DK}_v)\) is defined to be a family of edge disjoint directed cycles contained in \(\text{DK}_v\). The largest cardinality of such a packing will be denoted by \(p(v,m)\). The paper shows that for \(m =6, 8\) and 10, we have \(p(v,m) = B(v,m)\), where \(B(v,m) = \lceil v (v - 1)/m \rceil\) is an obvious upper bound for \(p(v,m)\). Hence, the values of \(p(v,m)\) are now known for all even \(m \leq 10\). Several results when \(m\) is even and greater than 10 are also presented.