= Multipartite hypergraph
A multipartite <hypergraph> has a specified partition of its <vertex of a hypergraph> <set> into parts, and every <hypergraph edge> meets each part in at most one <vertex of a hypergraph>. For an $r$-<uniform hypergraph> with $r$ parts, an <hypergraph edge> chooses exactly one <vertex of a hypergraph> from each part; its indicator is therefore a <function> on the <Cartesian product> of those parts. A quadripartite three-uniform <hypergraph> instead has four possible types of <hypergraph edge>, according to the omitted part. A choice of one <vertex of a hypergraph> from each of its four parts is a <three-uniform tetrahedron> exactly when all four triples are <hypergraph edges>. Specifying the parts makes both <subset density> and labelled counting precise.
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