Subhypergraph

More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1, V2,..., Vk-1 has a unique perfect matching.

Next, Meunier [Colorful subhypergraphs in Kneser hypergraphs, The Electronic Journal of Combinatorics, 2014] improved their result by proving that any properly colored general Kneser hypergraph #123;#92;rmKG#125;ʳ(#123;#92;mathcalH#125;) contains a large colorful r-partite subhypergraph provided that r is prime.