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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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References

K. Cameron, E.M. Eschen, C.T. Hoàng and R. Sritharan, The list partition problem for graphs, in Proc. of the ACM-SIAM Symposium on Discrete Algorithms – SODA 2004. ACM, New York and SIAM, Philadelphia (2004) 384–392.
M. Chudnovsky, N. Robertson, P. Seymour and R. Thomas, Strong Perfect Graph Theorem, in Perfect Graph Conjecture workshop. American Institute of Mathematics (2002).
Chvátal, V., Star-Cutsets and Perfect Graphs. J. Combin. Theory Ser. B 39 (1985) 189–199. CrossRef
de Figueiredo, C.M.H., Klein, S., Kohayakawa, Y. and Reed, B., Finding Skew Partitions Efficiently. J. Algorithms 37 (2000) 505–521. CrossRef
Feder, T. and Hell, P., List homomorphisms to reflexive graphs. J. Combin. Theory Ser. B 72 (1998) 236–250. CrossRef
T. Feder, P. Hell, S. Klein and R. Motwani, Complexity of graph partition problems, in Proc. of the 31st Annual ACM Symposium on Theory of Computing - STOC'99. Plenum Press, New York (1999) 464–472.
Feder, T., Hell, P., Klein, S. and Motwani, R., List Partitions. SIAM J. Discrete Math. 16 (2003) 449–478. CrossRef