Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Solving MINONES-2-SAT as fast as VERTEX COVER
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Polynomial kernels for proper interval completion and related problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Weak compositions and their applications to polynomial lower bounds for kernelization
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Kernels for packing and covering problems
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
Solving min ones 2-sat as fast as vertex cover
Theoretical Computer Science
Polynomial kernels for Proper Interval Completion and related problems
Information and Computation
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Given a graph G and an integer k, the 驴 Edge Completion/Editing/Deletion problem asks whether it is possible to add, edit, or delete at most k edges in G such that one obtains a graph that fulfills the property 驴. Edge modification problems have received considerable interest from a parameterized point of view. When parameterized by k, many of these problems turned out to be fixed-parameter tractable and some are known to admit polynomial kernelizations, i.e., efficient preprocessing with a size guarantee that is polynomial in k. This paper answers an open problem posed by Cai (IWPEC 2006), namely, whether the 驴 Edge Deletion problem, parameterized by the number of deletions, admits a polynomial kernelization when 驴 can be characterized by a finite set of forbidden induced subgraphs. We answer this question negatively based on recent work by Bodlaender et al. (ICALP 2008) which provided a framework for proving polynomial lower bounds for kernelizability. We present a graph H on seven vertices such that $\mathcal{H}$-free Edge Deletion and H-free Edge Editing do not admit polynomial kernelizations, unless $\mbox{NP}\subseteq \mbox{coNP}/\mbox{poly}$. The application of the framework is not immediate and requires a lower bound for a Not-1-in-3 SAT problem that may be of independent interest.