Explicit Two-Sided Vertex Expanders beyond the Spectral Barrier
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3717823.3718241.pdf
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Author(s)
Hsieh, Jun-Ting
Lin, Ting-Chun
Mohanty, Sidhanth
O'Donnell, Ryan
Zhang, Rachel Yun
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Jun-Ting Hsieh, Ting-Chun Lin, Sidhanth Mohanty, Ryan O'Donnell, and Rachel Yun Zhang. 2025. Explicit Two-Sided Vertex Expanders beyond the Spectral Barrier. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 833–842.
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Final published version
Abstract
We construct the first explicit two-sided vertex expanders that bypass the spectral barrier.
Previously, the strongest known explicit vertex expanders were given by d-regular Ramanujan graphs, whose spectral properties imply that every small subset of vertices S has at least 0.5d|S| distinct neighbors. However, it is possible to construct Ramanujan graphs containing a small set S with no more than 0.5d|S| neighbors. In fact, no explicit construction was known to break the 0.5 d-barrier.
In this work, we give an explicit construction of an infinite family of d-regular graphs (for large enough d) where every small set expands by a factor of ≈ 0.6d.
More generally, for large enough d1,d2, we give an infinite family of (d1,d2)-biregular graphs where small sets on the left expand by a factor of ≈ 0.6d1, and small sets on the right expand by a factor of ≈ 0.6d2. In fact, our construction satisfies an even stronger property: small sets on the left and right have unique-neighbor expansion 0.6d1 and 0.6d2 respectively.
Our construction follows the tripartite line product framework of Hsieh et. al., and instantiates it using the face-vertex incidence of the 4-dimensional Ramanujan clique complex as its base component. As a key part of our analysis, we derive new bounds on the triangle density of small sets in the Ramanujan clique complex.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/3717823.3718241
