Finding topological subgraphs is fixedparameter tractable
Abstract
We show that for every fixed undirected graph $H$, there is a $O(V(G)^3)$ time algorithm that tests, given a graph $G$, if $G$ contains $H$ as a topological subgraph (that is, a subdivision of $H$ is subgraph of $G$). This shows that topological subgraph testing is fixedparameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every $H$ we obtain an $O(V(G)^3)$ time algorithm that tests if there is an immersion of $H$ into a given graph $G$. This answers another open question raised by Downey and Fellows in 1992.
 Publication:

arXiv eprints
 Pub Date:
 November 2010
 arXiv:
 arXiv:1011.1827
 Bibcode:
 2010arXiv1011.1827G
 Keywords:

 Computer Science  Data Structures and Algorithms