# The undirected feedback vertex set problem has a Poly(k) Kernel

Burrage, Kevin, Estivill-Castro, Vladimir, Fellows, Michael R., Langston, Michael A., Macnamara, Shev, & Rosamond, Frances A.
(2006)
The undirected feedback vertex set problem has a Poly(k) Kernel. In
*Lecture Notes in Computer Science*, Springer Berlin / Heidelberg, Zurich, Switzerland, pp. 192-202.

## Abstract

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G', k') where k' � k, and the number of vertices of G' is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.

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ID Code: | 46190 |
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Item Type: | Conference Paper |

DOI: | 10.1007/11847250_18 |

ISSN: | 0302-9743 |

Subjects: | Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) (010104) |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Schools > Mathematical Sciences |

Copyright Owner: | Copyright 2006 Springer Verlag |

Deposited On: | 28 Sep 2011 01:59 |

Last Modified: | 29 Feb 2012 14:36 |

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