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arXiv · 2611.06813

The 3-Uniform Hyperclique Hypothesis is False

Timothy M. Chan·Reina Itakura·Zhiyuan Ma·Yuancheng Yu
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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 $k\ge 4$, and a faster exponential-time algorithm for Max-3-SAT.

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Timothy M. Chan, Reina Itakura, Zhiyuan Ma, Yuancheng Yu. 2026-11-04. The 3-Uniform Hyperclique Hypothesis is False. https://arxiv.org/abs/2611.06813

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