Geodesic
Graph Decompositions and Factorizing Permutations
Discrete mathematics & theoretical computer science, Tome 5 (2002).

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A factorizing permutation of a given graph is simply a permutation of the vertices in which all decomposition sets appear to be factors. Such a concept seems to play a central role in recent papers dealing with graph decomposition. It is applied here for modular decomposition and we propose a linear algorithm that computes the whole decomposition tree when a factorizing permutation is provided. This algorithm can be seen as a common generalization of Ma and Hsu 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. 
@article{DMTCS_2002_5_a4,
     author = {Capelle, Christian and Habib, Michel and Montgolfier, Fabien},
     title = {Graph {Decompositions} and {Factorizing} {Permutations}},
     journal = {Discrete mathematics & theoretical computer science},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.298/}
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Capelle, Christian; Habib, Michel; Montgolfier, Fabien. Graph Decompositions and Factorizing Permutations. Discrete mathematics & theoretical computer science, Tome 5 (2002). doi : 10.46298/dmtcs.298. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.298/

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