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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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Chan et al. (2026) studied this question.
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