A circular-arc model (C, A) is a circle C together with a collection A of arcs of C. If A satisfies the Helly Property then (C, 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Lin, M. C., & Szwarcfiter, J. L. (2006). Characterizations and linear time recognition of helly circular-arc graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 73–82). Springer Verlag. https://doi.org/10.1007/11809678_10
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