The complexity of the vertex-minor problem

Axel Dahlberg*, Jonas Helsen, Stephanie Wehner

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
22 Downloads (Pure)


A graph H is a vertex-minor of a graph G if it can be reached from G by the successive application of local complementations and vertex deletions. Vertex-minors have been the subject of intense study in graph theory over the last decades and have found applications in other fields such as quantum information theory. Therefore it is natural to consider the computational complexity of deciding whether a given graph G has a vertex-minor isomorphic to another graph H. Here we prove that this decision problem is NP-complete, even when restricting H and G to be circle graphs, a class of graphs that has a natural relation to vertex-minors.

Original languageEnglish
Article number106222
Number of pages8
JournalInformation Processing Letters
Publication statusPublished - 2022


  • Circle graphs
  • Computational complexity
  • NP-complete
  • Vertex-minor


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