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Paper:

TR14-051 | 12th April 2014 17:18

Hardness of Coloring $2$-Colorable $12$-Uniform Hypergraphs with $2^{(\log n)^{\Omega(1)}}$ Colors

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TR14-051
Authors: Subhash Khot, Rishi Saket
Publication: 12th April 2014 19:10
Downloads: 1272
Keywords: 


Abstract:

We show that it is quasi-NP-hard to color $2$-colorable $12$-uniform hypergraphs with $2^{(\log n)^{\Omega(1) }}$ colors where $n$ is the number of vertices. Previously, Guruswami et al. [GHHSV14] showed that it is quasi-NP-hard to color $2$-colorable $8$-uniform hypergraphs with $2^{2^{\Omega(\sqrt{\log \log n})}}$ colors. Their result is obtained by composing a standard Outer PCP with an Inner PCP based on the Short Code of super-constant degree. Our result is instead obtained by composing a new Outer PCP with an Inner PCP based on the Short Code of degree two.



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