Kneser graphs are like swiss cheese

Ehud Friedgut; Oded Regev

doi:10.19086/da3103

Kneser graphs are like swiss cheese

Ehud Friedgut, Oded Regev

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for a large family of product graphs, and for Kneser graphs K(n,αn) with fixed α < 1/2, the following holds. Any set of vertices that spans a small proportion of the edges in the graph can be made independent by removing a small proportion of the vertices of the graph. This allows us to strengthen the results of [3] and [2], and show that any independent set in these graphs is almost contained in an independent set which depends on few coordinates. Our proof is inspired by, and follows some of the main ideas of, Fox's proof of the graph removal lemma [6].

Original language	English (US)
Pages (from-to)	1-18
Number of pages	18
Journal	Discrete Analysis
Volume	2
Issue number	2018
DOIs	https://doi.org/10.19086/da3103
State	Published - 2018

Keywords

Independent set
Kneser graph
Product graphs

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.19086/da3103

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AB - We prove that for a large family of product graphs, and for Kneser graphs K(n,αn) with fixed α < 1/2, the following holds. Any set of vertices that spans a small proportion of the edges in the graph can be made independent by removing a small proportion of the vertices of the graph. This allows us to strengthen the results of [3] and [2], and show that any independent set in these graphs is almost contained in an independent set which depends on few coordinates. Our proof is inspired by, and follows some of the main ideas of, Fox's proof of the graph removal lemma [6].

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Kneser graphs are like swiss cheese

Abstract

Keywords

ASJC Scopus subject areas

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