Seminars on Discrete Mathematics: Chromatic, Homomorphism and Blowup thresholds

：黄欣祺（中国科学技术大学）
：2025-12-30 15:00
：海韵园实验楼S208

报告人：黄欣祺（中国科学技术大学）

时  间：2025年12月30日15:00

地  点：海韵园实验楼S208

内容摘要:

In 1973, Erdős and Simonovits initiated the study of minimum-degree conditions forcing H-free graphs to have bounded chromatic number, leading to the notion of the chromatic threshold of H. This problem attracted sustained attention for decades and was completely determined by Allen, Böttcher, Griffiths, Kohayakawa, and Morris in 2013.

A natural strengthening asks whether one can force not only bounded chromatic number (equivalently, a bounded-order homomorphic image), but a bounded-order homomorphic image that is itself H-free; this leads to the much less understood theory of homomorphism thresholds, originating from questions raised by Thomassen in 2002.

Motivated by these problems, we recently introduced a new notion, the blow-up threshold, which strengthens homomorphism-type conclusions by requiring a dense maximal H-free graph to arise as a blow-up of a bounded-order template. In this talk, we survey the history of these thresholds and present our recent progress.

个人简介：

黄欣祺，中国科学技术大学大学数学学院博士在读，指导老师为张先得教授、Tuan Tran教授，现于韩国基础科学研究院ECOPRO小组进行长期访问，导师为刘鸿教授。主要科研兴趣为极值图论、加性组合与编码理论。

 

联系人：陈继勇