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arXiv · 2611.01338

Threshold existence for random NAE-$k$-SAT and random hypergraph $2$-colourability

Pavel Zakharov
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Abstract

The existence of limiting threshold densities for random hypergraph $2$-colourability and random NAE-$k$-SAT was conjectured in earlier work, including Achlioptas and Moore [RANDOM 2002] and Coja-Oghlan and Panagiotou [STOC 2012]. We prove these conjectures for all $k\geq 3$. We also show that $α^{\mathrm{2-col}}_k \leq α^{\mathrm{NAE}}_k$ for each $k\geq 3$.

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Pavel Zakharov. 2026-10-31. Threshold existence for random NAE-$k$-SAT and random hypergraph $2$-colourability. https://arxiv.org/abs/2611.01338

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