Parallel recognition of doubly chordal graphs

The class of doubly chordal graphs is a subclass of chordal graphs and a superclass of strongly chordal graphs, which arise in many application areas. Many optimization problems like domination and Steiner tree which are NP-complete on, chordal graphs can be solved in polynomial time on doubly chordal graphs. We investigate several characterizations and properties of doubly chordal graphs. Using these properties we show that the recognition of a doubly chordal graph with n vertices and m edges and the generation of a doubly perfect elimination ordering can be done in O(log(2) 72) time using O(nm) processors on the CRCW PRAM model.