Improved Kernels for Edge Modification Problems
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In an edge modification problem, we are asked to modify at most k edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A great amount of efforts have been devoted to understanding the kernelization complexity of these problems. We revisit several well-studied edge modification problems, and develop improved kernels for them: * a 2 k-vertex kernel for the cluster edge deletion problem, * a 3 k^2-vertex kernel for the trivially perfect completion problem, * a 5 k^1.5-vertex kernel for the split completion problem and the split edge deletion problem, and * a 5 k^1.5-vertex kernel for the pseudo-split completion problem and the pseudo-split edge deletion problem. Moreover, our kernels for split completion and pseudo-split completion have only O(k^2.5) edges. Our results also include a 2 k-vertex kernel for the strong triadic closure problem, which is related to cluster edge deletion.
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