Ǩp,q-factorization of symmetric complete tripartite digraphs

Kazuhiko Ushio, Yoshikazu Ohtsubo
2001 Discrete Mathematics  
Let K * n 1 ;n 2 ;n 3 denote the symmetric complete tripartite digraph with partite sets V1; V2; V3 of n1; n2; n3 vertices each, and letKp;q denote the complete bipartite digraph in which all arcs are directed away from p start-vertices in Vi to q end-vertices in Vj with {i; j} ⊂{1; 2; 3}. We show that a necessary condition for the existence of aKp;q-factorization of K * n 1 ;n 2 ;n 3 is n1 = n2 = n3 ≡ 0 (mod dp q (p + q )) for p + q ≡ 1; 2 (mod 3) and n1 = n2 = n3 ≡ 0 (mod dp q (p + q )=3);
more » ... ¿pp ; 2n1¿qq for p + q ≡ 0 (mod 3), where d = (p; q); p = p=d; q = q=d. Several su cient conditions are also given.
doi:10.1016/s0012-365x(00)00339-3 fatcat:4lzdx4i3xrd7tpwrnw7jzgahsm