A Tur'an-type problem for circular arc graphs
  A circular arc graph is the intersection graph of a collection of connected arcs on the circle. We solve a Tur'an-type problem for circular arc graphs: for n arcs, if m and M are the minimum and maximum number of arcs that contain a common point, what is the maximum number of edges the circular arc graph can contain? We establish a sharp bound and produce a maximal construction. For a fixed m, this can be used to show that if the circular arc graph has enough edges, there must be a point that is covered by at least M arcs. In the case m=0, we recover results for interval graphs established by Abbott and Katchalski (1979). We suggest applications to voting situations with interval or circular political spectra. 
Rosalie Carlson, Stephen Flood, Kevin O'Neill, and Francis Edward Su
math.CO cs.DM