Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
Almost all k-colorable graphs are easy to color
Journal of Algorithms
The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
An O(n0.4)-approximation algorithm for 3-coloring
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Coloring heuristics for register allocation
PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Approximating maximum independent sets by excluding subgraphs
SWAT '90 Proceedings of the second Scandinavian workshop on Algorithm theory
Algorithms for approximate graph coloring
Algorithms for approximate graph coloring
A still better performance guarantee for approximate graph coloring
Information Processing Letters
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Register allocation & spilling via graph coloring
SIGPLAN '82 Proceedings of the 1982 SIGPLAN symposium on Compiler construction
Graphs and Hypergraphs
Randomized graph products, chromatic numbers, and Lovasz j-function
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Graph coloring algorithms for fast evaluation of Curtis decompositions
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Coloring k-colorable graphs using smaller palettes
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Coloring k-colorable graphs using relatively small palettes
Journal of Algorithms
Evaluation of Neural and Genetic Algorithms for Synthesizing Parallel Storage Schemes
International Journal of Parallel Programming
Approximate Coloring of Uniform Hypergraphs (Extended Abstract)
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Coloring 2-colorable hypergraphs with a sublinear number of colors
Nordic Journal of Computing
Approximate coloring of uniform hypergraphs
Journal of Algorithms
New approximation guarantee for chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Distributed channel management in uncoordinated wireless environments
Proceedings of the 12th annual international conference on Mobile computing and networking
Proceedings of the 10th annual conference on Genetic and evolutionary computation
On hard instances of approximate vertex cover
ACM Transactions on Algorithms (TALG)
Combinatorial optimization in system configuration design
Automation and Remote Control
Note: A simple algorithm for 4-coloring 3-colorable planar graphs
Theoretical Computer Science
Distributed coloring depending on the chromatic number or the neighborhood growth
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Linear index coding via semidefinite programming
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Symmetry breaking depending on the chromatic number or the neighborhood growth
Theoretical Computer Science
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The problem of coloring a graph with the minimum number of colorsis well known to be NP-hard, even restricted tok-colorable graphs for constantk ≥ 3. This paper explores theapproximation problem of coloringk-colorable graphs with as fewadditional colors as possible in polynomial time, with special focus onthe case of k = 3.The previous best upper bound on the number of colors needed forcoloring 3-colorable n-vertex graphsin polynomial time was on/logn colors by Berger and Rompel, improving a bound ofon colors by Wigderson. This paper presents an algorithmto color any 3-colorable graph with on3/8polylogn colors, thus breaking an“O((n1/2-&ogr;(1))barrier”. The algorithm given here is based on examiningsecond-order neighborhoods of vertices, rather than just immediateneighborhoods of vertices as in previous approaches. We extend ourresults to improve the worst-case bounds for coloringk-colorable graphs for constantk 3 as well.