Graph decompositions and factorizing permutations
نویسندگان
چکیده
A factorizing permutation of a given graph is simply a permutation of its vertices of which all decomposition sets are factors [3]. Such a concept appears to play a central role in recent papers dealing with graph decomposition. It is applied here for modular decomposition of directed graphs, and we propose a simple linear algorithm that computes the whole decomposition tree when a factorizing permutation is provided.
منابع مشابه
Reduced decompositions and permutation patterns
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملar X iv : m at h / 05 06 24 2 v 2 [ m at h . C O ] 1 2 Ju l 2 00 5 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملar X iv : m at h / 05 06 24 2 v 3 [ m at h . C O ] 1 7 Fe b 20 06 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملar X iv : m at h / 05 06 24 2 v 1 [ m at h . C O ] 1 3 Ju n 20 05 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملSimpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations
Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization problems. Accordingly, there has been a drive towards a practical, linear-time algorithm for the problem. This paper posits such an algorithm; we present a linear-time modular decomposi...
متن کامل