### Abstract

In the k-path problem we are given an n-vertex graph g together with an integer k and asked whether g contains a path of length k as a subgraph. We give the first subexponential time, polynomial space parameterized algorithm for k-path on planar graphs, and more generally, on h-minor-free graphs. The running time of our algorithm is o(2^{o(\sqrt{k}\log^2 k)}n^{o(1)})o(2^{o(\sqrt{k}\log^2 k)}n^{o(1)}).

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science |

Subtitle of host publication | 37th International Workshop, WG 2011 Tepla Monastery, Czech Republic, June 2011 Revised Papers |

Editors | Petr Kolman, Jan Kratochvil |

Publisher | Springer |

Pages | 262-270 |

ISBN (Electronic) | 978-3-642-25870-1 |

ISBN (Print) | 978-3-642-25869-5 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 6986 |

## Cite this

Lokshtanov, D., Mnich, M., & Saurabh, S. (2011). Planar k-Path in Subexponential Time and Polynomial Space. In P. Kolman, & J. Kratochvil (Eds.),

*Graph-Theoretic Concepts in Computer Science: 37th International Workshop, WG 2011 Tepla Monastery, Czech Republic, June 2011 Revised Papers*(pp. 262-270). Springer. Lecture Notes in Computer Science, Vol.. 6986 https://doi.org/10.1007/978-3-642-25870-1_24