The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Easy problems for tree-decomposable graphs
Journal of Algorithms
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
On the complexity of approximating the independent set problem
Information and Computation
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
Invitation to data reduction and problem kernelization
ACM SIGACT News
On Parameterized Path and Chordless Path Problems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On Two Problems in the Generation of Program Test Paths
IEEE Transactions on Software Engineering
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
On the complexity of paths avoiding forbidden pairs
Discrete Applied Mathematics
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
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Tight bounds for linkages in planar graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Kernelization of packing problems
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
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
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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.