Recognition of circular-arc graphs and some subclasses

In this work we present three new recognition algorithms for circular-arc graphs and for two subclasses of this graph class. We give a linear-time recognition algorithm for circular-arc graphs based on the algorithm of Eschen and Spinrad [ES93, Esc97]. Our algorithm is simpler than the earlier linear-time recognition algorithm of McConnell [McC03], which is the only linear time recognition algorithm previously known. We give new characterizations of proper circular-arc graphs and of unit circular-arc graphs which are based on characterizations of Tucker [Tuc71, Tuc74]. These characterizations lead to two new linear-time algorithms for recognizing proper circular-arc graphs and for recognizing unit circular-arc graphs. Both algorithms either provide a model for the input graph, or a certificate that such a model does not exist. No other previous algorithm for each of these two graph classes provides a certificate for its result.