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A Turing kernelization dichotomy for structural parameterizations of F-Minor-Free Deletion
Journal of Computer and System Sciences ( IF 1.1 ) Pub Date : 2021-03-03 , DOI: 10.1016/j.jcss.2021.02.005
Huib Donkers , Bart M.P. Jansen

For a fixed finite family of graphs F, the F-Minor-Free Deletion problem takes as input a graph G and integer and asks whether a size- vertex set X exists such that GX is F-minor-free. {K2}-Minor-Free Deletion and {K3}-Minor-Free Deletion encode Vertex Cover and Feedback Vertex Set respectively. When parameterized by the feedback vertex number of G these two problems are known to admit a polynomial kernelization. We show {P3}-Minor-Free Deletion parameterized by the feedback vertex number is MK[2]-hard. This rules out the existence of a polynomial kernel assuming NPcoNP/poly. Our hardness result generalizes to any F containing only graphs with a connected component of at least 3 vertices, using as parameter the vertex-deletion distance to treewidth mintw(F), where mintw(F) denotes the minimum treewidth of the graphs in F. For all other families F we present a polynomial Turing kernelization. Our results extend to F-Subgraph-Free Deletion.



中文翻译:

图灵核化二分法用于结构的参数化 F-次要删除

对于固定的有限图族 F, 这 F-Minor免费缺失问题作为输入的曲线图G ^和整数并询问一个大小-是否顶点集合X存在,使得G-XF-次要的。 {ķ2个}-次要删除{ķ3}-次要-自由删除分别对“顶点覆盖”和“反馈顶点集”进行编码。当由G的反馈顶点数进行参数化时,这两个问题已知可以进行多项式核化。我们展示{P3}由反馈顶点编号参数化的-次要-自由删除MK[2个]-难的。这排除了多项式内核的存在NP协同NP/。我们的硬度结果可以推广到任何F 仅包含具有至少3个顶点的连通分量的图,并使用到树宽的顶点删除距离作为参数 twF, 在哪里 twF 表示图中的最小树宽 F。对于其他所有家庭F我们提出了多项式图灵核化。我们的结果扩展到F-Subgraph-Free删除

更新日期:2021-03-09
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