Imbalances of bipartite multitournaments

Abstract. A bipartite \((a,b,p,q)\)-tournament is a bipartite tournament in which the parts of the tournament contain \(p\), resp. \(q\) vertices and the vertices belonging to different parts of the tournament are connected with at least \(a\) and at most \(b\) arcs. The imbalance of a vertex is defined as the difference of its outdegree and indegree. In this paper existence criteria and construction algorithms are presented for bipartite \((0,b,p,q)\)-tournaments having prescribed imbalance sequences and prescribed imbalance sets.