Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
On problems without polynomial kernels
Journal of Computer and System Sciences
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Lower Bounds for Kernelizations and Other Preprocessing Procedures
Theory of Computing Systems
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
European Journal of Combinatorics
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Complexity of the path avoiding forbidden pairs problem revisited
Discrete Applied Mathematics
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Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization lower bounds. This work explores the existence of polynomial kernels for various path and cycle problems, by considering nonstandard parameterizations. We show polynomial kernels when the parameters are a given vertex cover, a modulator to a cluster graph, or a (promised) max leaf number. We obtain lower bounds via cross-composition, e.g., for Hamiltonian Cycle and related problems when parameterized by a modulator to an outerplanar graph.