报告题目：Extremal density for subdivisions with length or sparsity constraints 

报告人：杨帆 山东大学

报告时间：5月20日 15：00

报告地点：五教5305

摘要：

Given a graph $H$, a balanced subdivision of $H$ is obtained by replacing all edges of $H$ with internally disjoint paths of the same length. In this paper, we prove that for any graph $H$, a linear-in-$e(H)$ bound on average degree guarantees a balanced $H$-subdivision. This strengthens an old result of Bollob\'as and Thomason, and resolves a question of Gil-Fern\'{a}ndez, Hyde, Liu, Pikhurko and Wu.

We observe that this linear bound on average degree is best possible whenever $H$ is logarithmically dense. We further show that this logarithmic density is the critical threshold: for many graphs $H$ below this density, its subdivisions are forcible by a sublinear-in-$e(H)$ bound on average degree. We provide such examples by proving that the subdivisions of any almost bipartite graph $H$ with sublogarithmic density

are forcible by a sublinear-in-$e(H)$ bound on average degree, provided that $H$ satisfies some additional separability condition. 

个人简介：

杨帆 ，2022年博士毕业于山东大学数学学院，导师是吴建良教授。2022-2025年在山东大学数据科学研究院从事博士后，合作导师是王光辉教授，2024年9月由国家留学基金委(CSC)资助赴韩国基础科学研究院(Institute for Basic Science)ECOPRO组从事博士后，合作导师是刘鸿教授。主持国家自然科学基金青年项目，山东省自然科学基金青年项目，在JLMS，JCTB，EJC等国际期刊共发表学术论文8篇。