We study the graph isomorphism problem for graph classes defined by sets of forbidden subgraphs. We show that there is a complexity dichotomy in case the set of forbidden subgraphs is finite. More precisely, we show that the problem is polynomial-time solvable if the forbidden set contains a forest of subdivided stars and is graph isomorphism complete otherwise. We also show that, assuming that the graph isomorphism problem is not polynomial-time solvable in general, there is no such dichotomy for the cases of infinite sets of forbidden subgraphs. To this end, we conditionally show that there exists a graph class closed under taking subgraphs with intermediate isomorphism problem, i.e., a class on which the isomorphism problem is neither polynomial-time solvable nor graph isomorphism complete. © 2013 Springer-Verlag.
CITATION STYLE
Otachi, Y., & Schweitzer, P. (2013). Isomorphism on subgraph-closed graph classes: A complexity dichotomy and intermediate graph classes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8283 LNCS, pp. 111–118). https://doi.org/10.1007/978-3-642-45030-3_11
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