A method to compute various upper bounds for the Clar number (defined as the number of circles in a Clar formula) of a benzenoid hydrocarbon is given. Based on this method two particular upper bounds are presented. For various examples, one of these bounds is sharp. Heuristic use of the method to find the Clar number of a given benzenoid hydrocarbon is also illustrated.
Published March 1992 , 16 pages