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Consider a family of chords in a circle. A circle graph is obtained by representing each chord by a vertex, two vertices being connected by an edge when the corresponding chords intersect. In this paper, we describe efficient algorithms for finding a maximum clique and a maximum independent set of circle graphs. These algorithms require at most n 3 steps, where n is the number of vertices in the graph.
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Fǎnicǎ Gavril (1973) studied this question.
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