an:03987295
Zbl 0611.05017
Robertson, Neil; Seymour, P. D.
Graph minors. II. Algorithmic aspects of tree-width
EN
J. Algorithms 7, 309-322 (1986).
00151980
1986
j
05C05 05C10 05C38 68R10
contractability; tree-width; polynomially bounded algorithm; planar graph; polynomial algorithm
[For part I see the authors' paper in J. Comb. Theory 35, 39-61 (1983; Zbl 0521.05062).]
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 \(\leq w\), 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.
Zbl 0598.05055; Zbl 0598.05042; Zbl 0548.05025; Zbl 0568.05025; Zbl 0521.05062