报告时间：2025年5月21日 9:30开始
报 告 人：王健（太原理工大学 副教授）
报告地点：腾讯会议：135-605-322
报告题目：Andrásfai-Erdős-Sós theorem for the generalized triangle
报告摘要: The celebrated Andrásfai-Erdős-Sós Theorem from 1974 shows that every n-vertex triangle-free graph with minimum degree greater than 2n/5 must be bipartite. Its extensions to 3-uniform hypergraphs without the generalized triangle F_5 = \{abc, abd, cde\} have been explored in several previous works, demonstrating the existence of \varepsilon > 0 such that for large n, every n-vertex F_5-free 3-graph with minimum degree greater than (1/9-\varepsilon) n^2 must be 3-partite.
We determine the optimal value for \varepsilon by showing that for n \ge 5000, every n-vertex F_5-free 3-graph with minimum degree greater than 4n^2/45 must be 3-partite, thus establishing the first tight Andrásfai-Erdős-Sós type theorem for hypergraphs. As a corollary, for all positive n, every n-vertex cancellative 3-graph with minimum degree greater than 4n^2/45 must be 3-partite. This result is also optimal and considerably strengthens prior work, such as that by Bollobas and Keevash--Mubayi. Joint work with Xizhi Liu and Sijie Ren.
报告人简介：王健，太原理工大学数学学院副教授，2016年博士毕业于南开大学组合数学中心，导师为陈永川院士。主要研究方向为极值组合学，在Combinatorics Probability and Computing，J. Combin. Theory Ser. A，J. Combin. Theory Ser. B，Journal of Graph Thoery， Siam Journal on Discrete Math.等期刊发表论文20余篇，主持国家自然科学基金两项。