报告题目：Uniform hypergraph independence bounds: from maximum degree to average degree

报告人：张俊驰 复旦大学

报告时间：5月25日下午2:00

报告地点：五教5205

摘要：We prove a transfer theorem for hereditary classes of $(r+1)$-uniform hypergraphs. Under a mild regularity hypothesis on a function $f$, a lower bound of the form $(1-o_\Delta(1))f(\Delta)/\Delta^{1/r}$ for independence number in terms of maximum degree implies the corresponding lower bound of the form $(1-o_d(1))f(d)/d^{1/r}$ in terms of average degree. In the logarithmic case, this recovers and unifies average-degree bounds for linear, locally sparse and uncrowded uniform hypergraphs. We also derive graph-theoretic consequences for locally $q$-colorable graphs, graphs excluding a fixed cycle, clique, bipartite graph, almost bipartite graph, or $3$-colorable graph.

个人介绍：张俊驰，复旦大学上海数学中心二年级博士生，导师为吴河辉教授，获2025中国科协青年博士生托举计划资助。