Implicit Enumeration of Topological-Minor-Embeddings and Its Application to Planar Subgraph Enumeration

11/18/2019

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by   Yu Nakahata, et al.

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Given graphs G and H, we propose a method to implicitly enumerate topological-minor-embeddings of H in G using decision diagrams. We show a useful application of our method to enumerating subgraphs characterized by forbidden topological minors, that is, planar, outerplanar, series-parallel, and cactus subgraphs. Computational experiments show that our method can find all planar subgraphs in a given graph at most five orders of magnitude faster than a naive backtracking-based method.