A. 481. Prove that there are infinitely many n, for which there exist simple graphs S1,...,Sn with the following properties:
(a) each Si is a complete bipartite graph;
(b) the union of the graphs S1,...,Sn is a complete graph on 2n vertices;
(c) each edge of this complete graph is contained in an odd number of the graphs Si.
Deadline expired on 15 May 2009.