2014/08/01 by Girish Varma, Varma, Girish · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Computational Geometry and Mesh Generation #Computer science #Discrete mathematics #FOS: Computer and information sciences #Graph #Hypergraph #Mathematics #Omega #Physics #Soundness #Vertex (graph theory) #cs.CC
paper · pdf · doi:10.48550/arxiv.1408.0262
openalex publication_date 2014/08/01 · arxiv created 2014/12/11 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness of coloring a 2-colorable 12-uniform hypergraph with 2^(log n)Ω(1) colors. This result was proved using a novel outer PCP verifier which had a strong soundness guarantee. In this note, we show that we can reduce the arity of their result by modifying their 12-query inner verifier to an 8-query inner verifier based on the hypergraph coloring hardness reductions of Guruswami et. al. [STOC 2014]. More precisely, we prove quasi-NP-hardness of the following problems on n-vertex hypergraphs. - Coloring a 2-colorable 8-uniform hypergraph with 2^(log n)Ω(1) colors. - Coloring a 4-colorable 4-uniform hypergraph with 2^(log n)Ω(1) colors.