Matchings in k-partite k-uniform Hypergraphs (Feb 17th, 2018)-计算...

MATCHINGS IN k-PARTITE k-UNIFORM HYPERGRAPHSJIE HAN, CHUANYUN ZANG, AND YI ZHAOAbstract. For k ≥ 3 and � > 0, let H be a k-partite k-graph with parts V1, . . . , Vk each of size n, where n is sufficiently large. Assume that for each i ∈ [k], every (k−1)-set in∏ j∈[k]\{i} Vi lies in at least ai edges, anda1 ≥ a2 ≥ · · · ≥ ak. We show that if a1, a2 ≥ �n, then H contains a matching of size min{n− 1, ∑i∈[k] ai}. In particular, H contains a matching of size n− 1 if each crossing (k− 1)-set lies in a