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

報 告 人：董子超

報告時間：2024年11月15日（周五）上午9：30-10：30

報告地點：騰訊會議 414-151-458

報告摘要: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 $p_0 = t - 1$.

報告人簡介：董子超，韓國基礎科學研究院（IBS）博士後，合作導師為劉鴻教授。2023年獲得美國卡耐基梅隆大學（CMU）博士學位，師從Boris Bukh教授，主要研究方向為極值組合學，在Siam Journal on Discrete Mathematics, Electronic journal of Combinatorics等雜志發表論文多篇。