报告题目：The perturbation threshold of degenerate graphs

报告摘要: In the past two decades, various properties of randomly perturbed/augmented (hyper)graphs have been intensively studied, since the model was introduced by Bohman, Frieze and Martin in 2003.The model usually considers a deterministic graphGwith minimum degree condition, perturbed/augmented by a binomial random graphG(n, p)on the same vertex set.

We show that for many problems of finding spanning subgraphs, one can indeed relax the minimum degree condition to a density condition: LetGbe ann-vertex graph with at leastΩ(n2)edges and letHbe ann-vertexd-degenerate graph with maximum degree at mostΔ. Then with high probability,G∪G(n,n−1/d−o(1))contains a copy ofH. This is a joint work with Jie Han, Seonghyuk Im and Junxue Zhang.

报告人简介：王斌，北京理工大学博士后，合作导师为韩杰教授。2024年博士毕业于巴黎萨克雷大学和山东大学，导师为李皓教授和王光辉教授。主要研究方向为极值图论与随机图论，在Forum of Mathematics, Sigma、SCIENCE CHINA Mathematics、SIAM Journal on Discrete Mathematics、DiscreteAppliedMathematics等期刊发表多篇文章。

报告时间：2026-01-27，10:40--11:40.

报告地点：明德楼C717

邀请人：王光辉，杨东雷