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Andreas Holmsen, Large cliques in hypergraphs with forbidden substructures

March 12 Tuesday @ 4:30 PM - 5:30 PM

Room B232, IBS (기초과학연구원)


Andreas Holmsen
Department of Mathematical Sciences, KAIST

A result due to Gyárfás, Hubenko, and Solymosi, answering a question of Erdős, asserts that if a graph $G$ does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\binom{n}{2}$ edges, then $G$ has a complete subgraph on at least $\frac{c^2}{10}n$ vertices. In this paper we suggest a “higher-dimensional” analogue of the notion of an induced $K_{2,2}$, which allows us to extend their result to $k$-uniform hypergraphs. Our result also has interesting consequences in topological combinatorics and abstract convexity, where it can be used to answer questions by Bukh, Kalai, and several others.


March 12 Tuesday
4:30 PM - 5:30 PM
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Room B232
IBS (기초과학연구원)


Sang-il Oum