On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Laplacian eigenvalues and the maximum cut problem
Mathematical Programming: Series A and B
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A sharp threshold for k-colorability
Random Structures & Algorithms
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Random MAX SAT, random MAX CUT, and their phase transitions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Colouring Random Graphs in Expected Polynomial Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
An Upper Bound for the Maximum Cut Mean Value
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT
Theoretical Computer Science
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
Approximating almost all instances of MAX-CUT within a ratio above the håstad threshold
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Coloring sparse random k-colorable graphs in polynomial expected time
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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We consider the MAX k-CUT problem in random graphs Gn,p. First, we estimate the probable weight of a MAX k-CUT using probabilistic counting arguments and byanaly zing a simple greedy heuristic. Then, we give an algorithm that approximates MAX k-CUT within expected polynomial time. The approximation ratio tends to 1 as np → ∞. As an application, we obtain an algorithm for approximating the chromatic number of Gn,p, 1/n ≤ p ≤ 1/2, within a factor of O(√np) in polynomial expected time, thereby answering a question of Krivelevich and Vu, and extending a result of Coja-Oghlan and Taraz. We give similar algorithms for random regular graphs Gn,r.