# Hypergraph independent sets

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4 Citations (Scopus)

### Abstract

The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is j-independent if its intersection with any edge has size strictly less than j. The Kruskal-Katona theorem implies that in an r-uniform hypergraph with a fixed size and order, the hypergraph with the most r-independent sets is the lexicographic hypergraph. In this paper, we use a hypergraph regularity lemma, along with a technique developed by Loh, Pikhurko and Sudakov, to give an asymptotically best possible upper bound on the number of j-independent sets in an r-uniform hypergraph.

Original language English 9-20 12 Combinatorics Probability and Computing 22 1 https://doi.org/10.1017/S0963548312000454 Published - 1 Jan 2013

### Fingerprint

Independent Set
Hypergraph
Uniform Hypergraph
Regularity Lemma
Extremal Problems
Strictly
Intersection
Upper bound
Imply
Subset
Theorem

### Cite this

Cutler, Jonathan ; Radcliffe, A. J. / Hypergraph independent sets. In: Combinatorics Probability and Computing. 2013 ; Vol. 22, No. 1. pp. 9-20.
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Hypergraph independent sets. / Cutler, Jonathan; Radcliffe, A. J.

In: Combinatorics Probability and Computing, Vol. 22, No. 1, 01.01.2013, p. 9-20.

Research output: Contribution to journalArticle

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