Kernel bounds for path and cycle problems

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25 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)117-136
Number of pages20
JournalTheoretical Computer Science
Volume511
DOIs
Publication statusPublished - 4 Nov 2013
Externally publishedYes

Keywords

  • Graphs
  • Kernelization
  • Parameterized complexity
  • Path and cycle problems
  • Upper and lower bounds

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