A better bound on the size of rainbow matchings

Aharoni and Howard conjectured that, for positive integers n,k,t with n≥kt, if F1,…,Ft⊆([n]k) such that |Fi|>max⁡{(nk)−(n−t+1k),(kt−1k)} for i∈[t] then there exist ei∈Fi for i∈[t] such that e1,…,et are pairwise disjoint. Huang, Loh, and Sudakov proved this conjecture for t更多