摘要
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.
Given integer k and a k-graph F,let tk-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 yk,lbe 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 tk-1(n,yk,l).In this paper,we show that tk-1(n,yk,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.
基金
Supported by NNSF of China(Grant No.11671376)
NSF of Anhui Province(Grant No.1708085MA18)
Anhui Initiative in Quantum Information Technologies(AHY150200)
