Untitled
An -vertex graph is called a small-set expander if any set of size ( ) contains at most a (1) fraction of the edges that touch it.The goal of this paper is to investigate small-set expansion properties of the Johnson graph, which is not a small-set expander.We obtain a qualitative descriptions of all small sets that violate the small-set expansion property in the Johnson graph: we show that any such set is correlated with some union of small intersections of "basic sets," where each basic set is a dictatorship-i.e., belonging to it depends only on containing a single coordinate .This condition is necessary and sufficient, since any such set violates the small-set expansion property.
Authors
- Muli Safra (ORCID: https://orcid.org/0000-0002-5022-7727)
- Dana Moshkovitz (ORCID: https://orcid.org/0000-0002-4151-568X)
- Dor Minzer (ORCID: https://orcid.org/0000-0002-8093-1328)
- Subhash Khot (ORCID: https://orcid.org/0009-0007-9246-4011)
Publication Details
- Journal
- Theory of Computing
- Published
- 2025-01-01
- DOI
- https://doi.org/10.4086/toc.2025.v021a002
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- European Commission
- Israel Science Foundation
- Tel Aviv University