no. 1
Finding H-partitions efficiently
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 133-144.

We study the concept of an H-partition of the vertex set of a graph G, which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H, with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties: non-list, 4-part, external constraints only (no internal constraints), each part non-empty. We describe tools that yield for each problem considered in this paper a simple and low complexity polynomial-time algorithm.

DOI : 10.1051/ita:2005008
Classification : 05C85, 68R10
Mots clés : structural graph theory, computational difficulty of problems, analysis of algorithms and problem complexity, perfect graphs, skew partition 
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     author = {Dantas, Simone and de Figueiredo, Celina M. H. and Gravier, Sylvain and Klein, Sulamita},
     title = {Finding $H$-partitions efficiently},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {133--144},
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Dantas, Simone; de Figueiredo, Celina M. H.; Gravier, Sylvain; Klein, Sulamita. Finding $H$-partitions efficiently. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 133-144. doi : 10.1051/ita:2005008. http://www.numdam.org/articles/10.1051/ita:2005008/

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