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Induced Minor Free Graphs: Isomorphism and Clique-width

  • Rémy Belmonte
  • Yota Otachi
  • Pascal Schweitzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

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 isomorphism complete. Additionally, we classify those graphs H for which H-induced-minor-free graphs have bounded clique-width. Those two results complement similar dichotomies for graphs that exclude a fixed graph as an induced subgraph, minor or subgraph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Rémy Belmonte
    • 1
  • Yota Otachi
    • 2
  • Pascal Schweitzer
    • 3
  1. 1.Department of Architectural EngineeringKyoto UniversityKyotoJapan
  2. 2.School of Information Science, Japan Advanced Institute of Science and TechnologyNomiJapan
  3. 3.RWTH Aachen UniversityAachenGermany

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