Deletion to scattered graph classes I - Case of finite number of graph classes

Ashwin Jacob, Jari J.H. de Kroon, Diptapriyo Majumdar, Venkatesh Raman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Graph-deletion problems involve deleting a small number of vertices so that the resulting graph belong to a given hereditary graph class. We initiate a study of a natural variation of the problem of deletion to scattered graph classes. We want to delete at most k vertices so that each connected component of the resulting graph belongs to one of the constant number of graph classes. As our main result, we show that this problem is non-uniformly fixed-parameter tractable (FPT) when the deletion problem corresponding to each of the constant number of graph classes is known to be FPT and the properties that a graph belongs to these classes are expressible in Counting Monodic Second Order (CMSO) logic. While this is shown using some black box theorems in parameterized complexity, we give a faster FPT algorithm when each of the graph classes has a finite forbidden set.

Original languageEnglish
Article number103460
JournalJournal of Computer and System Sciences
StatePublished - 1 Dec 2023


  • Fixed parameter tractability
  • Important separators
  • Parameterized complexity
  • Scattered graph classes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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