On chordal proper circular arc graphs (Q1322203)

A graph is an interval (circular arc) graph if it is the intersection graph of a family of intervals (arcs) on the real line (a circle). An interval (circular arc) graph is proper if the family of intervals (arcs) can be chosen to be inclusion-free. In the paper it is shown that a chordal graph is a proper interval graph if and only if it is claw-free, net-free and not a multiple of the tent. This result implies that a chordal graph is a proper circular arc graph if and only if it is claw-free and net-free.