Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
A still better performance guarantee for approximate graph coloring
Information Processing Letters
New approximation algorithms for graph coloring
Journal of the ACM (JACM)
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
Approximating coloring and maximum independent sets in 3-uniform hypergraphs
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
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Linear index coding via semidefinite programming
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Wireless capacity with arbitrary gain matrix
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
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We obtain the following new coloring results: • A 3-colorable graph on n vertices with maximum degree Δ can be colored, in polynomial time, using O((Δ log Δ)1/3 . log n) colors. This slightly improves an O((Δ1/3log1/2 Δ) . log n) bound given by Karger, Motwani, and Sudan. More generally, k-colorable graphs with maximum degree Δ can be colored, in polynomial time, using O((Δ1-2/klog1/k Δ) . log n) colors. • A 4-colorable graph on n vertices can be colored, in polynomial time, using O(n7/19) colors. This improves an O(n2/5) bound given again by Karger, Motwani, and Sudan. More generally, k-colorable graphs on n vertices can be colored, in polynomial time, using O(nαk) colors, where α5 = 97/207, α6 = 43/79, α7 = 1391/2315, α8 = 175/271 ..... The first result is obtained by a slightly more refined probabilistic analysis of the semidefinite programming based coloring algorithm of Karger, Motwani, and Sudan. The second result is obtained by combining the coloring algorithm of Karger, Motwani, and Sudan, the combinatorial coloring algorithms of Blum and an extension of a technique of Alon and Kahale (which is based on the Karger, Motwani, and Sudan algorithm) for finding relatively large independent sets in graphs that are guaranteed to have very large independent sets. The extension of the Alon and Kahale result may be of independent interest.