2020/08/27 by Bowtell, Candida, Hyde, Joseph
#05C07 #05C35 #05C65 #05C70 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.12222
The study of asymptotic minimum degree thresholds that force matchings and tilings in hypergraphs is a lively area of research in combinatorics. A key breakthrough in this area was a result of Hàn, Person and Schacht who proved that the asymptotic minimum vertex degree threshold for a perfect matching in an n-vertex 3-graph is ((5)/(9)+o(1))\binomn2. In this paper we improve on this result, giving a family of degree sequence results, all of which imply the result of Hàn, Person and Schacht, and additionally allow one third of the vertices to have degree (1)/(9)\binomn2 below this threshold. Furthermore, we show that this result is, in some sense, tight.