Efficient algorithms for interval graphs and circular‐arc graphs

Abstract

Abstract We show that for an interval graph given in the form of a family of intervals, a maximum independent set, a minimum covering by disjoint completely connected sets or cliques, and a maximum clique can all be found in O ( n log n ) time [ O ( n ) time if the endpoints of the intervals are sorted]. For the more general circular‐arc graphs, a maximum independent set and a minimum covering by disjoint completely connected sets or cliques can be found in O ( n 2 ) time, provided again that a corresponding family of arcs is given.