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Chordal Deletion is Fixed-Parameter Tractable

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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).

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Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Dániel Marx

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  1. Dániel Marx
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Correspondence to Dániel Marx.

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Research is supported by the Magyary Zoltán Felsőoktatási Közalapítvány and the Hungarian National Research Fund (OTKA grant 67651).

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Marx, D. Chordal Deletion is Fixed-Parameter Tractable. Algorithmica 57, 747–768 (2010). https://doi.org/10.1007/s00453-008-9233-8

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