报告人：丁来浩 博士
报告题目：F-factors in quasi-random hypergraphs
报告时间：2022年1月22日 上午9：00
报告地点：腾讯会议 ID：751 120 086
报告人简介：
丁来浩, 华中师范大学数学与统计学学院讲师, 硕士生导师, 2018 年博士毕业于山东大学, 2016 年 9 月-2017 年 9 月访问佐治亚理工学院. 目前主持国家自然科学基金青年基金1 项。研究方向主要包括图染色理论和极值图论, 在European Journal of Combinatorics , Discrete Mathematics , Science China Mathematics 等期刊上发表论文10 篇.
报告摘要：
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 talk, we introduce 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.
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