Abstract
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.
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