2021/10/31 by Lu, Hongliang, Wang, Yan, Yu, Xingxing
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.00372
Let k and n be two integers, with k≥ 3, n≡ 0\pmod k, and n sufficiently large. We determine the (k-1)-degree threshold for the existence of a rainbow perfect matchings in n-vertex k-uniform hypergraph. This implies the result of Rödl, Ruciński, and Szemerédi on the (k-1)-degree threshold for the existence of perfect matchings in n-vertex k-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of Rödl, Ruciński, and Szemerédi.