Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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DMTCS vol 5 no 1 (2002), pp. 55-70

Discrete Mathematics & Theoretical Computer Science


Volume 5 n° 1 (2002), pp. 55-70

author:Christian Capelle and Michel Habib and Fabien de Montgolfier
title:Graph Decompositions and Factorizing Permutations
keywords:Graph algorithms, graph decompositions, modular decomposition
abstract:A factorizing permutation of a given graph is simply a permutation of its vertices of which all decomposition sets are factors. 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. The approach of using parenthesized factors of a list was first used by Hopcroft and Tarjan for triconnected components search . Our algorithm can be seen as a common generalization of Hsu and Ma for modular decomposition of chordal graphs and Habib, Huchard and Spinrad for inheritance graphs decomposition. It also suggests many new decomposition algorithms for various notions of graph decompositions.

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reference: Christian Capelle and Michel Habib and Fabien de Montgolfier (2002), Graph Decompositions andFactorizing Permutations, Discrete Mathematics and Theoretical Computer Science 5, pp. 55-70
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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Automatically produced on Wed Apr 24 22:46:01 CEST 2002 by ifalk