### Abstract

We introduce an invariant of graphs called the tree-width, and use it to obtain a polynomially bounded algorithm to test if a graph has a subgraph contractible to H, where H is any fixed planar graph. We also nonconstructively prove the existence of a polynomial algorithm to test if a graph has tree-width ≤ w, for fixed w. Neither of these is a practical algorithm, as the exponents of the polynomials are large. Both algorithms are derived from a polynomial algorithm for the DISJOINT CONNECTING PATHS problem (with the number of paths fixed), for graphs of bounded tree-width.

Original language | English (US) |
---|---|

Pages (from-to) | 309-322 |

Number of pages | 14 |

Journal | Journal of Algorithms |

Volume | 7 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics

## Fingerprint Dive into the research topics of 'Graph minors. II. Algorithmic aspects of tree-width'. Together they form a unique fingerprint.

## Cite this

Robertson, N., & Seymour, P. D. (1986). Graph minors. II. Algorithmic aspects of tree-width.

*Journal of Algorithms*,*7*(3), 309-322. https://doi.org/10.1016/0196-6774(86)90023-4