The Undirected Feedback Vertex Set Problem Has a Poly(k) Kernel

  • Kevin Burrage
  • Vladimir Estivill-Castro
  • Michael Fellows
  • Michael Langston
  • Shev Mac
  • Frances Rosamond
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


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(k 11) kernelization bound.


Polynomial Time Vertex Cover Internal Vertex Reduction Rule Vertex Cover Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kevin Burrage
    • 1
  • Vladimir Estivill-Castro
    • 2
  • Michael Fellows
    • 3
  • Michael Langston
    • 4
    • 5
  • Shev Mac
    • 1
  • Frances Rosamond
    • 6
  1. 1.Department of MathematicsUniversity of QueenslandBrisbane
  2. 2.Griffith UniversityBrisbaneAustralia
  3. 3.School of EE & CSUniversity of NewcastleCallaghanAustralia
  4. 4.Department of Computer ScienceUniversity of TennesseeKnoxvilleUSA
  5. 5.Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA
  6. 6.The Retreat for the Arts and SciencesNewcastleAustralia

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