### 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 | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Independent set
- Kneser graph
- Product graphs

### ASJC Scopus subject areas

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Discrete Analysis*,

*2*(2018), 1-18. https://doi.org/10.19086/da3103

**Kneser graphs are like swiss cheese.** / Friedgut, Ehud; Regev, Oded.

Research output: Contribution to journal › Article

*Discrete Analysis*, vol. 2, no. 2018, pp. 1-18. https://doi.org/10.19086/da3103

}

TY - JOUR

T1 - Kneser graphs are like swiss cheese

AU - Friedgut, Ehud

AU - Regev, Oded

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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].

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].

KW - Independent set

KW - Kneser graph

KW - Product graphs

UR - http://www.scopus.com/inward/record.url?scp=85049659849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049659849&partnerID=8YFLogxK

U2 - 10.19086/da3103

DO - 10.19086/da3103

M3 - Article

AN - SCOPUS:85049659849

VL - 2

SP - 1

EP - 18

JO - Discrete Analysis

JF - Discrete Analysis

SN - 2397-3129

IS - 2018

ER -