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 Θ ( n 3.5 log n ) ; 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.
Published Version
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