Counting Triangles in Regular Graphs

：何家林（香港科技大学）
：2025-05-26 10:30
：海韵园行政楼C610

报告人：何家林（香港科技大学）

时  间：2025年5月26日10:30

地  点：海韵园行政楼C610

内容摘要:

We investigate the minimum number of triangles, denoted by t(n,k), in n-vertex k-regular graphs, where n is an odd integer and k is an even integer. The well-known Andrásfai-Erdős-Sós Theorem has established that t(n,k)>0 if k>2n/5. In a striking work, Lo has provided the exact value of t(n,k) for sufficiently large n, given that 2n/5+12√n/5<k<n/2. Here, we bridge the gap between the aforementioned results by determining the precise value of t(n,k) in the entire range 2n/5<k<n/2. This confirms a conjecture of Cambie, de Joannis de Verclos, and Kang for sufficiently large n. This is a joint work with Jie Ma, Xinmin Hou, and Tianying Xie. 

个人简介：

何家林，本科与博士均毕业于中国科学技术大学。博士导师为马杰教授，目前在香港科技大学数学系跟随王可教授做博士后。主要研究方向为极值图论中的图兰类问题，现已在领域期刊 JCTB，JGT 等共发表论文 5 篇。

联系人：靳宇