学术报告

       报告：Maximizing the number of cliques in a graph of given degree sequence $\ell^p$-norm

       时间：2024年11月01日10：30-11：30

       地点：长安校区教东B1-105

       邀请人：李若楠

       摘要：Suppose $1 \le p \le \infty$. For a simple graph $G$ with a vertex-degree sequence $d_1, \dots, d_n$ satisfying $(d_1^p + \dots + d_n^p)^{1/p} \le C$, we prove asymptotically sharp upper bounds on the number of $t$-cliques in $G$. This result bridges the $p = 1$ case, which is equivalent to the notable Kruskal--Katona theorem, and the $p = \infty$ case, known as the Gan--Loh--Sudakov conjecture, and resolved by Chase. In particular, we demonstrate that the extremal construction exhibits a dichotomy between a single clique and multiple cliques at $p_0 = t - 1$.

       报告人简介：董子超，韩国基础科学研究院博士后，合作导师为刘鸿教授。2023年获得美国卡耐基梅隆大学博士学位。主要从事极值组合学方面的研究，目前有2篇成果发表在《SIAM Journal on Discrete Mathematics》。