Homogeneity vs. Adjacency: generalising some graph decomposition algorithms Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien de Montgolfier To cite this version: Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien de Montgolfier. Homogeneity vs. Ad- jacency: generalising some graph decomposition algorithms. WG: Graph-Theoretic Concepts in Com- puter Science, Jun 2006, Bergen, Norway. pp.278-288, 10.1007/11917496_25. hal-00020188 HAL Id: hal-00020188 https://hal.archives-ouvertes.fr/hal-00020188 Submitted on 13 Mar 2006 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Homogeneity vs. Adjacency: generalising some graph decomposition algorithms B.-M. Bui Xuan1, M. Habib2, V. Limouzy2, and F. de Montgolfier2 1 LIRMM, Universit´eMontpellier 2, France.
[email protected] 2 LIAFA, Universit´eParis 7, France. {habib,limouzy,fm}@liafa.jussieu.fr Abstract. In this paper, a new general decomposition theory inspired from modular graph decompo- sition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular de- composition of directed graphs or decomposition of 2-structures, but also star cutsets and bimodular decomposition.