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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 269 - Combinatorics Seminar
Dr. Jiaxi Nie
Georgia Institute of Technology
Generalized Erdos-Rogers problems for hypergraphs
Abstract:
Given $r$-uniform hypergraphs $G$ and $F$ and an integer $n$, let $f_{F,G}(n)$ be the maximum $m$ such that every $n$-vertex $G$-free $r$-graph has an $F$-free induced subgraph on $m$ vertices. We show that $f_{F,G}(n)$ is polynomial in $n$ when $G$ is a subgraph of an iterated blowup of $F$. As a partial converse, we show that if $G$ is not a subgraph of an $F$-iterated blowup and is $2$-tightly connected, then $f_{F,G}(n)$ is at most polylogarithmic in $n$. Our bounds generalize previous results of Dudek and Mubayi for the case when $F$ and $G$ are complete. Joint work with Xiaoyu He.
May 6, 2025
2:00 PM
APM 7321
Research Areas
Combinatorics****************************
