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
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
Approximating coloring and maximum independent sets in 3-uniform hypergraphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
On the Hardness of 4-Coloring a 3-Colorable Graph
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Approximate Coloring of Uniform Hypergraphs
Approximate Coloring of Uniform Hypergraphs
Hardware-assisted view-dependent map simplification
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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We obtain the following new coloring results:A 3-colorable graph on n vertices with maximum degree &Dgr; can be colored, in polynomial time, using &Ogr;((&Dgr; log &Dgr;)1/3 ·log n) colors. This slightly improves an &Ogr;((&Dgr;1/3 log½ &Dgr;) · log n) bound given by Karger, Motwani and Sudan. More generally, k-colorable graphs with maximum degree &Dgr; can be colored, in polynomial time, using &Ogr;((&Dgr;1-2/k log1/k &Dgr;) · log n) colors.A 4-colorable graph on n vertices can be colored, in polynomial time, using &Ogr;(n7/19) colors. This improves an &Ogr;(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 &Ogr;(n&agr;k) colors, where &agr;5 = 97/207, &agr;6 = 43/79, &agr;7 = 1391/2315, &agr;8 = 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.