Elsevier

Journal of Algorithms

Volume 7, Issue 3, September 1986, Pages 309-322
Journal of Algorithms

Graph minors. II. Algorithmic aspects of tree-width

https://doi.org/10.1016/0196-6774(86)90023-4Get rights and content

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.

References (17)

There are more references available in the full text version of this article.

Cited by (0)

Research partially supported by NSF Grant MCS 8103440. Present address: Bell Communications Research. Inc., Morris Research and Engineering Center, 435 South Street, Morristown, New Jersey 07960.

View full text