Large Cliques in Hypergraphs with Forbidden Substructures

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A result due to Gyarfas, Hubenko, and Solymosi (answering a question of Erd}os) states that if a graph G on n vertices does not contain K2;2 as an induced subgraph yet has at least c n 2 edges, then G has a complete subgraph on at least c2 10 n vertices. In this paper we suggest a \higher-dimensional" analogue of the notion of an induced K2;2 which allows us to generalize their result to k-uniform hypergraphs. Our result also has an interesting consequence in discrete geometry. In particular, it implies that the fractional Helly theorem can be derived as a purely combinatorial consequence of the colorful Helly theorem
Publisher
SPRINGER HEIDELBERG
Issue Date
2020-08
Language
English
Article Type
Article
Citation

COMBINATORICA, v.40, no.4, pp.527 - 537

ISSN
0209-9683
DOI
10.1007/s00493-019-4169-y
URI
http://hdl.handle.net/10203/279573
Appears in Collection
MA-Journal Papers(저널논문)
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