document: Orthogonal decompositions of complete digraphs A family G of isomorphic copies of a given digraph G is said to be an orthogonal decomposition of the complete digraph D/sub n / by G , if every arc of D/sub n / belongs to exactly one member of G and the union of any two different elements from G contains precisely one pair of reverse arcs . Given a digraph h , an h family mh is the vertex-disjoint union of m copies of h . In this paper , we consider orthogonal decompositions by h-families . Our objective is to prove the existence of such an orthogonal decomposition whenever certain necessary conditions hold and m is sufficiently large
doc_bio_tags: B I O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O
extractive_keyphrases: orthogonal decompositions complete digraphs isomorphic copies necessary conditions
abstractive_keyphrases: vertex-disjoint union