an:00176761
Zbl 0764.68122
Lagergren, Jens; Arnborg, Stefan
Finding minimal forbidden minors using a finite congruence
EN
Automata, languages and programming, Proc. 18th Int. Colloq., Madrid/Spain 1991, Lect. Notes Comput. Sci. 510, 532-543 (1991).
1991
a
68R10 68T10 05C35 05C05 05C38
linear time algorithm; minimal forbidden minors; graphs of bounded tree- width; finite congruence; bound
Summary: [For the entire collection see Zbl 0753.00027.]
We give an effective way to compute the minimal forbidden minors for a minor-closed class of graphs of bounded tree-width from an algorithm that decides a finite congruence that recognizes the class. We prove constructively that every minor closed class of graphs of bounded tree- width that is recognized by a finite congruence has a finite number of minimal forbidden minors. Our proof gives a bound of the size of a minimal forbidden minor. We define explicitly a relation \(\sim\), prove that it is a finite congruence that recognizes the graphs of tree-width at most \(w\), and show how to decide it. Hence, we can find the minimal forbidden minors for graphs of tree-width at most \(w\) and bounds on their sizes. An algorithm that recognizes graphs of tree-width at most \(w\) in linear time is also obtained.
Zbl 0753.00027