MAX CUT in cubic graphs

Authors:
Eran Halperin;Dror Livnat;Uri Zwick
Affiliations:
Computer Science Division, University of California at Berkeley, Berkeley, CA;School of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel;School of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel
Venue:
Journal of Algorithms
Year:
2004

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Abstract

We present an improved semidefinite programming based approximation algorithm for the MAX CUT problem in graphs of maximum degree at most 3. The approximation ratio of the new algorithm is at least 0.9326. This improves, and also somewhat simplifies, a result of Feige, Karpinski and Langberg. We also observe that results of Hopkins and Staton and of Bondy and Locke yield a simple combinatorial 4/5-approximation algorithm for the problem. Finally, we present a combinatorial 22/27-approximation algorithm for the MAX CUT problem for regular cubic graphs.