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Approximation algorithms for max-bisection on low degree regular graphs. (English) Zbl 1102.68095
Summary: The max-bisection problem is to find a partition of the vertices of a graph into two equal size subsets that maximizes the number of edges with endpoints in both subsets. We obtain new improved approximation ratios for the max-bisection problem on the low degree \(k\)-regular graphs for \(3\leq k\leq 8\), by deriving some improved transformations from a maximum cut into a maximum bisection. In the case of three regular graphs we obtain an approximation ratio of 0.854, and in the case of four and five regular graphs, approximation ratios of 0.805, and 0.812, respectively.

68R10 Graph theory (including graph drawing) in computer science
68W25 Approximation algorithms
graph bisection