r-Multihypergraphs with prescribed edge degree sequences

A finite hypergraph in which the multiplicity of edges does not exceed r is called an r-multihypergraph. A necessary and sufficient condition for existence of r-multihypergraphs with prescribed edge degree sequence is given (Theorem 1). Previously obtained results for simple hypergraphs and multihypergraphs directly follow from Theorem 1 in boundary cases r = 1 and r = ∞.