Kernel bounds for path and cycle problems

Conference Contribution

Bodlaender, Hans L., Jansen, B.M.P. & Kratsch, Stefan (2012). Kernel bounds for path and cycle problems. Parameterized and Exact Computation - 6th International Symposium, IPEC 2011, Revised Selected Papers (pp. 145-158). (Lecture Notes in Computer Science, No. 7112). In Scopus Cited 11 times.

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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.