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) |
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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