Theory of Computing Systems

, Volume 64, Issue 2, pp 251–271 | Cite as

On the Parameterized Complexity of Graph Modification to First-Order Logic Properties

  • Fedor V. Fomin
  • Petr A. GolovachEmail author
  • Dimitrios M. Thilikos


We establish connections between parameterized/kernelization complexity of graph modification problems and expressibility in logic. For a first-order logic formula φ, we consider the problem of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the resulting modification has the property expressible by φ. We provide sufficient and necessary conditions on the structure of the prefix of φ specifying when the corresponding graph modification problem is fixed-parameter tractable (parameterized by k) and when it admits a polynomial kernel.


First-order logic Graph modification Parameterized complexity Descriptive complexity Kernelization 



We are grateful to Pål Drange for his very helpful remarks.


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Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.AlGCo Project Team, CNRS, LIRMMUniversité de MontpellierMontpellierFrance

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