Characterizations and linear time recognition of Helly circular-arc graphs

MIN CHIH LIN; JAYME L. SZWARCFITER

Taipei, Taiwan

Conferencia; COCOON'06 (12th Annual International Computing and Combinatorics Conference); 2006

Academia Sinica, Taiwan

A circular-arc model is a circle C together with a collection of arcs of C. If satisfies the Helly Property then 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.