Characterizations and linear time recognition of helly circular-arc graphs

  • Authors:

  • Min Chih Lin;Jayme L. Szwarcfiter

  • Affiliations:

  • Departamento de Computación, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Buenos Aires, Argentina;Instituto de Matemática, NCE, and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brasil

  • Venue:
  • COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
  • Year:
  • 2006

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Abstract

A circular-arc model $(C, \cal A)$ is a circle C together with a collection $\cal A$ of arcs of C. If $\cal A$ satisfies the Helly Property then $(C, \cal A)$ is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention, in the literature. Linear time recognition algorithm have been described both for the general class and for some of its subclasses. However, for Helly circular-arc graphs, the best recognition algorithm is that by Gavril, whose complexity is O(n3). In this article, we describe different characterizations for Helly circular-arc graphs, including a characterization by forbidden induced subgraphs for the class. The characterizations lead to a linear time recognition algorithm for recognizing graphs of this class. The algorithm also produces certificates for a negative answer, by exhibiting a forbidden subgraph of it, within this same bound.