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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)

Speaker

Andreas Holmsen
Department of Mathematical Sciences, KAIST
http://mathsci.kaist.ac.kr/~andreash/

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.

Details

Date:
March 12 Tuesday
Time:
4:30 PM - 5:30 PM
Event Category:
Event Tags:

Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
Discrete Mathematics Group (DIMAG)
Center for Mathematical and Computational Sciences
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr
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