Richard Beigel, David Eppstein

We consider worst case time bounds for NP-complete problems

including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring.

Our algorithms are based on a common generalization of these problems,

called symbol-system satisfiability or, briefly, SSS [R. Floyd &

R. Beigel, The Language of Machines]. 3-SAT is equivalent to

(2,3)-SSS while the other problems ...
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Irit Dinur, Elchanan Mossel, Oded Regev

We study the approximate-coloring(q,Q) problem: Given a graph G, decide

whether \chi(G) \le q or \chi(G)\ge Q. We derive conditional

hardness for this problem for any constant 3\le q < Q. For q \ge

4, our result is based on Khot's 2-to-1 conjecture [Khot'02].

For q=3, we base our hardness ...
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Subhash Khot, Rishi Saket

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 ... more >>>