Consider a family of chords i n a c ircle . is obtained by representing each chord by a vertex, two vertices being connected by an edge when the corresponding chords intersect. I n t h i s paper, we describe e f f i c i en t algorithms for finding a ma3cimwn clique and a maximum independent s e t of circle graphs. the number of vertices i n the graph. Key WO&: Circle graph, transi t ive graph, ...