Sven Hartmann
Orthogonal decompositions of complete digraphs
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
05C70 Factorization, matching, covering and packing
05B30 Other designs, configurations, See also {51E30}
Abstract: A family $\mathcal{G}$ of isomorphic copies of a given digraph $\dG$ is said
to be an orthogonal decomposition of the complete digraph $\dD_n$ by
$\dG$, if every arc of $\dD_n$ belongs to exactly two members of
$\mathcal{G}$ and the union of any two different elements from $\mathcal{G}$
contains precisely one pair of reverse arcs.

Given a digraph $\dH$, an $\dH$-family $m\dH$ is the vertex-disjoint union
of $m$ copies of $\dH$. In this paper, we consider orthogonal decompositions
by $\dH$-families. Our objective is to prove the existence of such an
orthogonal decomposition whenever certain necessary conditions hold and $m$
is sufficiently large.
Keywords: orthogonal; decomposition; ODC