Unifying two Graph Decompositions with Modular Decomposition
<|reference_start|>Unifying two Graph Decompositions with Modular Decomposition: We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation when the tree exists. Our results unify many known decomposition like modular and bi-join decomposition of graphs, and a new decomposition of tournaments.<|reference_end|>
@article{bui-xuan2006unifying,
    title={Unifying two Graph Decompositions with Modular Decomposition},
    author={Binh-Minh Bui-Xuan (LIRMM), Michel Habib (LIAFA), Vincent Limouzy
  (LIAFA), Fabien De Montgolfier (LIAFA)},
    journal={Dans Lecture Notes in Computer Science - International Symposium
  on Algorithms and Computation (ISAAC, Sendai : Japon (2007)},
    year={2006},
    doi={10.1007/978-3-540-77120-3},
    archivePrefix={arXiv},
    eprint={cs/0604065},
    primaryClass={cs.DS}
}