# A stability result for the cube edge isoperimetric inequality

Keevash, P
Long, E

April 2018

## Journal:

Journal of Combinatorial Theory: Series A

## Last Updated:

2019-04-27T06:15:49.6+01:00

155

## DOI:

10.1016/j.jcta.2017.11.005

360-375

## abstract:

We prove the following stability version of the edge isoperimetric inequality
for the cube: any subset of the cube with average boundary degree within $K$ of
the minimum possible is $\varepsilon$-close to a union of $L$ disjoint cubes,
where $L \leq L(K,\varepsilon )$ is independent of the dimension. This extends
a stability result of Ellis, and can viewed as a dimension-free version of
Friedgut's junta theorem.

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