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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Notes
- 1.
Since the acceptance of this paper for the publication in the conference proceedings, a preprint has become available addressing the graph isomorphism problem for graphs of bounded clique width [12].
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Belmonte, R., Otachi, Y., Schweitzer, P. (2016). Induced Minor Free Graphs: Isomorphism and Clique-width. In: Mayr, E. (eds) Graph-Theoretic Concepts in Computer Science. WG 2015. Lecture Notes in Computer Science(), vol 9224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53174-7_21
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DOI: https://doi.org/10.1007/978-3-662-53174-7_21
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