Intersection problems on perfect matchings of complete uniform hypergraphs are high order extremal problems. Let  be a complete -uniform hypergraph on  vertices. A family of perfect matchings of  is said to be -intersecting if any two members of this family have at leastedges in common. We provide an Erdős-Ko-Rado theorem for -intersecting families, improving a result proved by Meagher and Moura, and also show a Hilton-Milner theorem for perfect matchings.

姚天, 河南科技学院讲师, 2022年6月在北京师范大学取得理学博士学位. 研究兴趣为极值组合学, 成果发表于J. Combin. Theory Ser A, Discrete Math. 等期刊。