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I'm looking for properties of circular-arc graphs, mainly its equivalence relations with more common graph classes. Simular to properties such as $\mathit{interval} \equiv \mathit{chordal} \cap \mathit{cocomparability}$, $\mathit{interval} \subset \mathit{circular\_arc}$

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You might find the book Graph Classes: A Survey, A. Brandstadt, Van Bang Le and Jeremy Spinrad published by SIAM, 1999, of use. – Joseph Malkevitch Feb 10 '12 at 15:58

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