A note on hardness of promise hypergraph colouring
Marcin Wrochna
TL;DR
This work recast the result in the algebraic framework for Promise CSPs, using only a weaker version of the PCP theorem, to show that for all c-colouring of a 2-coloruable 3-uniform hypergraph, it is NP-hard to find a 1-coloured hypergraph.
Abstract
We show a slightly simpler proof the following theorem by I. Dinur, O. Regev, and C. Smyth: for all $c \geq 2$, it is NP-hard to find a $c$-colouring of a 2-coloruable 3-uniform hypergraph. We recast this result in the algebraic framework for Promise CSPs, using only a weaker version of the PCP theorem.