Asymptotic results on suborthogonal \(\overrightarrow{\mathfrak G}\)-decompositions of complete digraphs
Suppose \(K_n\) is the complete digraph on \(n\) vertices for any positive integer \(n\). A \(\overrightarrow{\mathfrak G}\)-decomposition of \(K_n\) is a partition of \(K_n\) into a family of isomorphic copies, called pages, of \(\overrightarrow{\mathfrak G}\). If the union of any two distinct pages contains at most one pair of reverse arcs, a \(\overrightarrow{\mathfrak G}\)-decomposition is suborthogonal. The author establishes that there exists a suborthogonal \(\overrightarrow{\mathfrak G}\)-decomposition of \(K_n\) for all sufficiently large \(n\) satisfying certain necessary conditions. It is known that given the same necessary conditions a \(\overrightarrow{\mathfrak G}\)-decomposition of \(K_n\) exists.
\(\overrightarrow{\mathfrak G}\)-decomposition
scientific article; zbMATH DE number 1340644