A note on hardness of promise hypergraph colouring
Marcin Wrochna

TL;DR
This paper simplifies the proof of NP-hardness for coloring certain hypergraphs, extending the algebraic framework for Promise CSPs with a weaker PCP theorem.
Contribution
It provides a simpler proof of a known NP-hardness result for hypergraph coloring within the Promise CSPs framework.
Findings
NP-hardness of c-coloring 2-colorable 3-uniform hypergraphs for all c ≥ 2
Recasts existing proof in algebraic Promise CSPs framework
Uses a weaker version of the PCP theorem
Abstract
We show a slightly simpler proof the following theorem by I. Dinur, O. Regev, and C. Smyth: for all , it is NP-hard to find a -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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · graph theory and CDMA systems
