
On the Parallel Parameterized Complexity of the Graph Isomorphism Problem
In this paper, we study the parallel and the space complexity of the gra...
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Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph th...
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Experimental Evaluation of Parameterized Algorithms for Graph Separation Problems: HalfIntegral Relaxations and Matroidbased Kernelization
In the recent years we have witnessed a rapid development of new algorit...
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On the Parameterized Complexity of Deletion to Hfree Strong Components
Directed Feedback Vertex Set (DFVS) is a fundamental computational prob...
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FixedParameter Tractability of Graph Deletion Problems over Data Streams
In this work, we initiate a systematic study of parameterized streaming ...
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Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations
We investigate polynomialtime preprocessing for the problem of hitting ...
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Parameterized Complexity of Fair Vertex Evaluation Problems
A prototypical graph problem is centered around a graph theoretic proper...
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Preprocessing VertexDeletion Problems: Characterizing Graph Properties by LowRank Adjacencies
We consider the Πfree Deletion problem parameterized by the size of a vertex cover, for a range of graph properties Π. Given an input graph G, this problem asks whether there is a subset of at most k vertices whose removal ensures the resulting graph does not contain a graph from Π as induced subgraph. Many vertexdeletion problems such as Perfect Deletion, Wheelfree Deletion, and Interval Deletion fit into this framework. We introduce the concept of characterizing a graph property Π by lowrank adjacencies, and use it as the cornerstone of a general kernelization theorem for ΠFree Deletion parameterized by the size of a vertex cover. The resulting framework captures problems such as ATFree Deletion, Wheelfree Deletion, and Interval Deletion. Moreover, our new framework shows that the vertexdeletion problem to perfect graphs has a polynomial kernel when parameterized by vertex cover, thereby resolving an open question by Fomin et al. [JCSS 2014]. Our main technical contribution shows how linearalgebraic dependence of suitably defined vectors over F_2 implies graphtheoretic statements about the presence of forbidden induced subgraphs.
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