The 3-Uniform Hyperclique Hypothesis is False
Timothy M. Chan, Reina Itakura, Zhiyuan Ma, Yuancheng Yu
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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