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- W2949183120 abstract "In a graph $G=(V,E)$, a bisection $(X,Y)$ is a partition of $V$ into sets $X$ and $Y$ such that $|X|le |Y|le |X|+1$. The size of $(X,Y)$ is the number of edges between $X$ and $Y$. In the Max Bisection problem we are given a graph $G=(V,E)$ and are required to find a bisection of maximum size. It is not hard to see that $lceil |E|/2 rceil$ is a tight lower bound on the maximum size of a bisection of $G$. We study parameterized complexity of the following parameterized problem called Max Bisection above Tight Lower Bound (Max-Bisec-ATLB): decide whether a graph $G=(V,E)$ has a bisection of size at least $lceil |E|/2 rceil+k,$ where $k$ is the parameter. We show that this parameterized problem has a kernel with $O(k^2)$ vertices and $O(k^3)$ edges, i.e., every instance of Max-Bisec-ATLB is equivalent to an instance of Max-Bisec-ATLB on a graph with at most $O(k^2)$ vertices and $O(k^3)$ edges." @default.
- W2949183120 created "2019-06-27" @default.
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- W2949183120 date "2010-05-17" @default.
- W2949183120 modified "2023-10-18" @default.
- W2949183120 title "Note on Maximal Bisection above Tight Lower Bound" @default.
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- W2949183120 doi "https://doi.org/10.48550/arxiv.1005.2848" @default.
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