Approximation and Intractability Results for the Maximum Cut Problem and Its Variants
IEEE Transactions on Computers
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On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Note on maximal bisection above tight lower bound
Information Processing Letters
Journal of Computer and System Sciences
Solving MAX-r-SAT Above a Tight Lower Bound
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Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
Max-cut parameterized above the edwards-erdős bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Parameterized Complexity
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
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A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most one, and the size of the bisection is the number of edges which go across the two parts. Every graph with m edges has a bisection of size at least ⌈m/2 ⌉, and this bound is sharp for infinitely many graphs. Therefore, Gutin and Yeo considered the parameterized complexity of deciding whether an input graph with m edges has a bisection of size at least ⌈m/2 ⌉+k, where k is the parameter. They showed fixed-parameter tractability of this problem, and gave a kernel with O(k2) vertices. Here, we improve the kernel size to O(k) vertices. Under the Exponential Time Hypothesis, this result is best possible up to constant factors.