Bipartite three-uniform hypergraph
= Bipartite three-uniform hypergraph
A three-<uniform hypergraph> is bipartite when its vertex set has a partition into two parts such that every <hyperedge> meets both parts. All such triples on parts of sizes $a,b$ number $a\binom b2+b\binom a2=ab(a+b-2)/2$. For fixed total order this is maximized by balanced parts.