报告时间：2024年11月26日 15:00开始
报 告 人：李佳傲（南开大学 教授）
报告地点：9-218
报告题目：The circular flow number of random regular graphs
报告摘要：For positive integers $s, t$ with $s\ge 2t$, a circular $s/t$-flow of a graph $G$ is defined as a pair $(D, f)$ where $D$ represents an orientation of $G$, and $f$ is a function mapping the edges of $G$ to the set $\{\pm t, \pm (t+1), \ldots, \pm (s-t)\}$ such that, at each vertex, the sum of the $f$-values of the incoming edges equals the sum of the $f$-values of the outgoing edges. The circular flow number of $G$, denoted by $\phi(G)$, is the infimum among all $s/t$ such that $G$ admits a circular $s/t$-flow. It follows from a result of Robinson and Wormald (RSA 1992) that a random $3$-regular graph $G$ is a.s.s. $3$-edge-colorable and thus $\phi(G)\le 4$. Pralat and Wormald (JGT 2020) proved that a random $5$-regular graph $G$ a.s.s. has $\phi(G)\le 3$. Alon and Pralat (CPC 2011) showed that for large enough $p$, a random $(4p+1)$-regular graph $G$ a.s.s. has $\phi(G)\le 2+1/p$. In this paper, applying tools from maxcuts and Tutte orientations, we improve the result of Alon and Pralat (CPC 2011) by proving that for large enough integer $k$, a random $(2k+1)$-regular graph $G$ a.s.s. satisfies $\phi(G)=2+\frac{2}{k}-(1+o_{k}(1))\frac{2\sqrt{2}C}{k\sqrt{k}}$, where $C\approx 0.763$ is an explicit constant.
报告人简介：李佳傲，南开大学数学科学麻豆视频av，教授，博士生导师。本科和硕士毕业于中国科学技术大学，博士毕业于美国西弗吉尼亚大学（导师为赖虹建教授），之后入职南开大学，历任讲师、副教授，2022年12月至今任教授。主要研究兴趣是离散数学与组合图论。包括图的染色，Tutte整数流理论，图结构与分解，加性组合，网络与组合优化等问题。已完成和发表论文三十余篇，研究成果发表在J. Combin. Theory Ser. B, SIAM J. Discrete Math, J. Graph Theory 等杂志。担任天津市数学会秘书长，中国运筹学会图论组合分会理事，以及SCI杂志Journal of Combinatorial Optimization的副编辑（Associate Editor）等学术兼职。入选天津市“131”创新型人才培养工程第三层次(2019)，天津市青年人才托举工程(2020)，南开大学百名青年学科带头人培养计划(2021)。2022年获国家自然科学基金优秀青年科学基金项目资助，2024年获中国运筹学会青年科技奖。
