AbstractConsider a finite family of non‐empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect. The intersection graph of a family of arcs on a circularly ordered set is called a circular‐arc graph. In this paper we give a characterization of the circular‐arc graph and we describe efficient algorithms for recognizing two subclasses. Also, we describe efficient algorithms for finding a maximum independent set, a minimum covering by cliques and a maximum clique of a circular‐arc graph.