# Finding topological subgraphs is fixed-parameter tractable

@inproceedings{Grohe2010FindingTS, title={Finding topological subgraphs is fixed-parameter tractable}, author={Martin Grohe and Ken-ichi Kawarabayashi and D{\'a}niel Marx and Paul Wollan}, booktitle={STOC '11}, year={2010} }

We prove that for every fixed undirected graph <i>H</i>, there is an O(|V(G)|<sup>3</sup>) time algorithm that, given a graph <i>G</i>, tests if <i>G</i> contains <i>H</i> as a topological subgraph (that is, a subdivision of <i>H</i> is subgraph of <i>G</i>). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every <i>H</i> we obtain an O(|V(G)|<sup>3</sup>) time algorithm that… CONTINUE READING

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Finding topological subgraphs is fixed-parameter tractable

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## The Directed Subgraph Homeomorphism Problem

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## Fixed-parameter intractability

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## Parameterized Complexity

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