Edge separators of planar and outerplanar graphs with applications
Journal of Algorithms
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Towards a syntactic characterization of PTAS
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A note on approximating Max-Bisection on regular graphs
Information Processing Letters
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation of max-cut on graphs of bounded degree
Journal of Algorithms
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Polynomial Time Approximation Schemes for MAX-BISECTION on Planar and Geometric Graphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Derandomizing semidefinite programming based approximation algorithms
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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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≤k≤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.