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Discrete Applied Mathematics
Volume 154, Issue 13, 15 August 2006, Pages 1783-1790
Traces of the Latin American Conference on Combinatorics, Graphs and Applications - A selection of papers from LACGA 2004, Santiago, Chile
 
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doi:10.1016/j.dam.2006.03.022    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2006 Published by Elsevier B.V.

Algorithms for clique-independent sets on subclasses of circular-arc graphs

Guillermo Durána, 1, E-mail The Corresponding Author, Min Chih Linb, 2, E-mail The Corresponding Author, Sergio Merab, 2, E-mail The Corresponding Author and Jayme Luiz Szwarcfiterc, 3, E-mail The Corresponding Author

aDepartamento de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile bDepartamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina cInstituto de Matemática, NCE and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil

Received 21 December 2004; 
revised 5 August 2005; 
accepted 18 January 2006. 
Available online 18 May 2006.

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Abstract

A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a View the MathML source-free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n2). These algorithms suppose that an HCA model of the graph is given.

Keywords: Algorithms; Circular-arc graphs; Clique-independent sets; Helly circular-arc graphs

Article Outline

1. Introduction
2. Intersection segments
3. Algorithms for clique-independent sets
4. Conclusions
References

Discrete Applied Mathematics
Volume 154, Issue 13, 15 August 2006, Pages 1783-1790
Traces of the Latin American Conference on Combinatorics, Graphs and Applications - A selection of papers from LACGA 2004, Santiago, Chile
 
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