, Volume 80, Issue 1, pp 29–47 | Cite as

Induced Minor Free Graphs: Isomorphism and Clique-Width

  • Rémy Belmonte
  • Yota Otachi
  • Pascal  Schweitzer


Given two graphs G and H, we say that G contains H as an induced minor if a graph isomorphic to H can be obtained from G by a sequence of vertex deletions and edge contractions. We study the complexity of Graph Isomorphism on graphs that exclude a fixed graph as an induced minor. More precisely, we determine for every graph H that Graph Isomorphism is polynomial-time solvable on H-induced-minor-free graphs or that it is GI-complete. Additionally, we classify those graphs H for which H-induced-minor-free graphs have bounded clique-width. These two results complement similar dichotomies for graphs that exclude a fixed graph as an induced subgraph, minor, or subgraph.


Induced minor Graph isomorphism Clique-width 



The authors thank the anonymous reviewers for constructive comments that improved the presentation of the paper.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Rémy Belmonte
    • 1
  • Yota Otachi
    • 2
  • Pascal  Schweitzer
    • 3
  1. 1.University of Electro-CommunicationsTokyoJapan
  2. 2.Japan Advanced Institute of Science and TechnologyIshikawaJapan
  3. 3.RWTH Aachen UniversityAachenGermany

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