Algorithmica

, Volume 57, Issue 4, pp 747–768 | Cite as

Chordal Deletion is Fixed-Parameter Tractable

Article

Abstract

It is known to be NP-hard to decide whether a graph can be made chordal by the deletion of k vertices or by the deletion of k edges. Here we present a uniformly polynomial-time algorithm for both problems: the running time is f(k)⋅n α for some constant α not depending on k and some f depending only on k. For large values of n, such an algorithm is much better than trying all the O(n k ) possibilities. Therefore, the chordal deletion problem parameterized by the number k of vertices or edges to be deleted is fixed-parameter tractable. This answers an open question of Cai (Discrete Appl. Math. 127:415–429, 2003).

Keywords

Chordal graphs Fixed-parameter tractability Chordal deletion 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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