Circular-arc graph for distinct distances
= Circular-arc graph for distinct distances
Around each of $n$ points draw its at most $t$ distinct-distance <circles>. On every <circle> containing at least three points, join cyclically consecutive points by arcs. The resulting loopless <multigraph> has at least $n(n-1)-2nt$ <edges> and a drawing with $O(n^2t^2)$ crossings. A pair joined by several arcs has every corresponding centre on its <perpendicular bisector>, which is the key to bounding multiplicity.