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25th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
December 4-8, 2000
University of Canterbury
Christchurch, New Zealand

Organizers
Charles Semple, Mike Steel

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Evenly partite bigraph-factorization of symmetric complete tripartite multi-digraphs
by
Kazuhiko Ushio
Kinki University
Coauthors: Hideaki Fujimoto (Kinki University)

We show that the necessary and sufficient condition for the existence of a [`K]p, 2q - factorization of the symmetric complete tripartite multi-digraph \lambdaK*n1, n2, n3 is

  1. n1=n2=n3 \equiv 0 (mod p) for p=q,

  2. n1=n2=n3 \equiv 0 (mod d(p'+2q')p'q'/e) for p =/= q and p' odd,

  3. n1=n2=n3 \equiv 0 (mod 2d(p''+q')p''q'/e') for p =/= q and p'=2p'',
where d=(p, q), p'=p/d, q'=q/d, e=(\lambda, p'q'), and e'=(\lambda, p''q').

Date received: August 9, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafn-05.