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The Clique Algorithm

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The Clique Algorithm

Authored by Ashay Dharwadker

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.

Publication Date:
1466391219 / 9781466391215
Page Count:
Binding Type:
US Trade Paper
Trim Size:
8.5" x 11"
Full Color
Related Categories:
Computers / Computer Science

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