The Clique Algorithm (Paperback) (ISBN-13: 9781466391215)

We present a new polynomial-time algorithm for finding maximal cliques in graphs. As a corollary, we obtain new bounds on the famous Ramsey numbers in terms of the maximum and minimum vertex degrees of the corresponding Ramsey graphs. The algorithm finds a maximum clique in all known examples of graphs. In view of the importance of the P versus NP question, we ask if there exists a graph for which the algorithm cannot find a maximum clique. The algorithm is demonstrated by finding maximum cliques for several famous graphs, including two large benchmark graphs with hidden maximum cliques. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.

Author: Ashay Dharwadker
ISBN-10: 1466391219
ISBN-13: 9781466391215
Publisher: Createspace Independent Publishing Platform
Language: English
Published: 10/02/2011
Pages: 48
Format: Paperback
Weight: 0.30lbs
Size: 11.00h x 8.50w x 0.12d