Restricted circular-arc graphs and clique cycles (Q1869213)

A circular-arc graph is the intersection graph of a system of circular arcs in the plane. It is Helly, if it has the property that whenever every two arcs in the mentioned system \({\mathcal A}\) have a point in common, then so have all arcs of \({\mathcal A}\). It is said to be restricted, if and only if it satisfies the following two conditions: (A1) The points of \({\mathcal A}\) are not covered by three of fewer arcs in \({\mathcal A}\). (A2) If \(p\), \(p'\) are endpoints of an arc in \({\mathcal A}\), then there is an arc in \({\mathcal A}\) that contains \(p\) but not \(p'\). These concepts are studied and compared with analogous concepts for the so-called clique trees.