# The 3-Uniform Hyperclique Hypothesis is False

“The 3-Uniform Hyperclique Hypothesis is False” (2026), by Timothy M. Chan et al. Computer Science research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Timothy M. Chan, Reina Itakura, Zhiyuan Ma, Yuancheng Yu
- Published: November 4, 2026
- Field: Computer Science
- DOI: https://doi.org/10.48550/arxiv.2611.06813
- Free PDF: https://arxiv.org/pdf/2611.06813

## Abstract

We present truly subquartic algorithms for detecting or counting 4-hypercliques in a 3-uniform hypergraph with n vertices, disproving a popular hypothesis in fine-grained complexity. The result immediately implies a faster algorithm for finding a k-hyperclique in a 3-uniform hypergraph for all constant k≥ 4, and a faster exponential-time algorithm for Max-3-SAT.

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