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Finding H-partitions efficiently

Published online by Cambridge University Press:  15 March 2005

Simone Dantas ,
Celina M.H. de Figueiredo ,
Sylvain Gravier  and
Sulamita Klein
Simone Dantas
Affiliation:
Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, CEP 13084-971, Campinas, SP, Brasil; [email protected]
Celina M.H. de Figueiredo
Affiliation:
Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP 21945-970, Rio de Janeiro, RJ, Brasil; [email protected] & [email protected]
Sylvain Gravier
Affiliation:
CNRS, GeoD research group, “Maths à modeler” project, Laboratoire Leibniz, France; [email protected]
Sulamita Klein
Affiliation:
Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP 21945-970, Rio de Janeiro, RJ, Brasil; [email protected] & [email protected]
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Abstract

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.

Keywords

Structural graph theorycomputational difficulty of problemsanalysis of algorithms and problem complexityperfect graphsskew partition
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 133 - 144
Copyright
© EDP Sciences, 2005

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