The complexity of counting homeomorphs (Q1058852)
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scientific article; zbMATH DE number 3902036
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The complexity of counting homeomorphs |
scientific article; zbMATH DE number 3902036 |
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The complexity of counting homeomorphs (English)
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1985
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In this note we show that, for any finite nontrivial family \({\mathcal H}\) of graphs, the problem of finding the number of subgraphs of a graph which are homeomorphic from a member of \({\mathcal H}\) is {\#}P-complete. From this it follows that the problems of counting the paths, circuits, or minimal nonplanar subgraphs of a graph are all {\#}P-complete.
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sharp-P-completeness
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number of subgraphs
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paths
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circuits
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minimal nonplanar subgraphs
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