2021/08/18 by Laihao Ding, Ding, Laihao, Jie Han +7 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2108.10731
openalex publication_date 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given k≥ 2 and two k-graphs (k-uniform hypergraphs) F and H, an F-factor in H is a set of vertex-disjoint copies of F that together covers the vertex set of H. Lenz and Mubayi [J. Combin. Theory Ser. B, 2016] studied the F-factor problem in quasi-random k-graphs with minimum degree Ω(nk-1). They posed the problem of characterizing the k-graphs F such that every sufficiently large quasi-random k-graph with constant edge density and minimum degree Ω(nk-1) contains an F-factor, and in particular, they showed that all linear k-graphs satisfy this property. In this paper we prove a general theorem on F-factors which reduces the F-factor problem of Lenz and Mubayi to a natural sub-problem, that is, the F-cover problem. By using this result, we answer the question of Lenz and Mubayi for those F which are k-partite k-graphs, and for all 3-graphs F, separately. Our characterization result on 3-graphs is motivated by the recent work of Reiher, Rödl and Schacht [J. Lond. Math. Soc., 2018] that classifies the 3-graphs with vanishing Turán density in quasi-random k-graphs.