Independent sets in regular graphs and sum-free subsets of finite groups

Noga Alon

doi:10.1007/BF02772952

Independent sets in regular graphs and sum-free subsets of finite groups

Noga Alon

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

90 Scopus citations

Abstract

It is shown that there exists a function ∈(k) which tends to 0 as k tends to infinity, such that any k-regular graph on n vertices contains at most 2^{(1/2+∈(k))n} independent sets. This settles a conjecture of A. Granville and has several applications in Combinatorial Group Theory.

Original language	English (US)
Pages (from-to)	247-256
Number of pages	10
Journal	Israel Journal of Mathematics
Volume	73
Issue number	2
DOIs	https://doi.org/10.1007/BF02772952
State	Published - Jun 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02772952

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abstract = "It is shown that there exists a function ∈(k) which tends to 0 as k tends to infinity, such that any k-regular graph on n vertices contains at most 2(1/2+∈(k))n independent sets. This settles a conjecture of A. Granville and has several applications in Combinatorial Group Theory.",

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AB - It is shown that there exists a function ∈(k) which tends to 0 as k tends to infinity, such that any k-regular graph on n vertices contains at most 2(1/2+∈(k))n independent sets. This settles a conjecture of A. Granville and has several applications in Combinatorial Group Theory.

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Independent sets in regular graphs and sum-free subsets of finite groups

Abstract

All Science Journal Classification (ASJC) codes

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