Codegree Threshold for Tiling k-graphs with Two Edges Sharing Exactly ℓ Vertices

Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an F-factor.For integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph with two edges that shares exactly l vertices.Han and Zhao(J.Combin.Theory Ser.A,(2015))asked the following question:For all k≥3,0≤l≤k-1 and sufficiently large n divisible by 2 k-l,determine the exact value of t_k-1(n,y(k,l)).In this paper,we show that t(k-1)(n,y(k,l))=n/(2 k-l)for k>3 and 1≤l≤k-2,combining with two previously known results of R?dl,Rucinski and Szemeredi(J.Combin.Theory Ser.A,(2009))and Gao,Han and Zhao(Combinatorics,Probability and Computing,(2019)),the question of Han and Zhao is solved completely.