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 (n3.5 log n); but the best combinatorial algorithms have approximation ratio 4/5 only, achieved in O (n2) 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 (n2) time, perhaps improvable even to O (n). Our main tool is a new type of vertex decomposition for graphs of maximum degree 3.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics