An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Coloring k-colorable graphs using relatively small palettes
Journal of Algorithms
On the Hardness of 4-Coloring a 3-Colorable Graph
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Improved hardness results for approximating the chromatic number
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Unique Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New approximation guarantee for chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the fourier tails of bounded functions over the discrete cube
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the tractability of coloring semirandom graphs
Information Processing Letters
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Improved Inapproximability Results for Maximum k-Colorable Subgraph
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Hypergraph Dictatorship Test with Perfect Completeness
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Note: A simple algorithm for 4-coloring 3-colorable planar graphs
Theoretical Computer Science
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
On unique games with negativeweights
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Bounds on locally testable codes with unique tests
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Parallel Repetition in Projection Games and a Concentration Bound
SIAM Journal on Computing
Majority is stablest: discrete and SoS
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We study the APPROXCOLORING q(Q) problem: Given a graph G, decide whether χ(G) ≤ q or χ(G) ≥ Q. We derive conditional hardness for this problem for any constant 3 ≤ q ε is hard for any constant ε0, assuming Khot's Unique Games conjecture. This is the problem of deciding for a given graph, between the case where one can 3-color all but a ε fraction of the vertices without monochromatic edges, and the case where the graph contains no independent set of relative size at least ε.Our result is based on bounding various generalized noise-stability quantities using the invariance principle of Mossel et al [MOO'05].