A Note on Distinct-Factorizations

Abstract

An $S_{s,t}$ distar-factorization of $D{K}_m$ is an edge partitioning of the complete symmetric directed graph $D{K}_m$ into subdigraphs each of which is isomorphic to the distar $S_{s,t}$ (the distar $S_{s,t}$ being obtained from the star $K_{1,s+t}$ by directing $s$ of the edges into the centre and $t$ of the edges out of the centre). We consider the question, “When can the arcs of $D{K}_m$ be partitioned into arc-disjoint subgraphs each isomorphic to $S_{s,t}$?” and give necessary and sufficient conditions for $S_{s,t}$ distar-factorizations of $D{K}_m$ in the cases when either $m\equiv 0$ or $1(\mathrm{mod}s+t)$.