Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3

Authors:
Cristina Bazgan;Zsolt Tuza
Affiliations:
LAMSADE, Université Paris-Dauphine, Place du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France;Computer and Automation Institute, Hungarian Academy of Sciences, Kende u. 13-17, H-1111 Budapest, Hungary and Department of Computer Science, University of Pannonia, Egyetem u. 10, H-8200 Veszpr& ...
Venue:
Journal of Discrete Algorithms
Year:
2008

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Abstract

The best approximation algorithm for Max Cut in graphs of maximum degree 3 uses semidefinite programming, has approximation ratio 0.9326, and its running time is @Q(n^3^.^5logn); but the best combinatorial algorithms have approximation ratio 4/5 only, achieved in O(n^2) time [J.A. Bondy, S.C. Locke, J. Graph Theory 10 (1986) 477-504; E. Halperin, et al., J. Algorithms 53 (2004) 169-185]. Here we present an improved combinatorial approximation, which is a 5/6-approximation algorithm that runs in O(n^2) time, perhaps improvable even to O(n). Our main tool is a new type of vertex decomposition for graphs of maximum degree 3.