6 research outputs found
Star-factorization of symmetric complete bipartite multi-digraphs
AbstractWe show that a necessary and sufficient condition for the existence of an Sk-factorization of the symmetric complete bipartite multi-digraph λKm,n∗ is m=n≡0(modk(k−1)/d), where d=(λ,k−1)
Cycle-factorization of symmetric complete multipartite digraphs
AbstractFirst, we show that a necessary and sufficient condition for the existence of a C3-factorization of the symmetric tripartite digraph Kn1,n2,n3∗, is n1 = n2 = n3. Next, we show that a necessary and sufficient condition for the existence of a C̄2k-factorization of the symmetric complete multipartite digraph Kn1, n2,…,nm is n1 = n2 = … = nm = 0 (mod k) for even m and n1 = n2 = … = ≡ 0 (mod 2k) for odd m
Transitive path decompositions of Cartesian products of complete graphs
An -decomposition of a graph is a partition of its edge set into
subgraphs isomorphic to . A transitive decomposition is a special kind of
-decomposition that is highly symmetrical in the sense that the subgraphs
(copies of ) are preserved and transitively permuted by a group of
automorphisms of . This paper concerns transitive -decompositions of
the graph where is a path. When is an odd prime, we
present a construction for a transitive path decomposition where the paths in
the decomposition are arbitrary large.Comment: 14 pages, 4 figure