{ "item_title" : "The Clique Algorithm", "item_author" : [" Ashay Dharwadker "], "item_description" : "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.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/1/46/639/121/1466391219_b.jpg", "price_data" : { "retail_price" : "15.00", "online_price" : "15.00", "our_price" : "15.00", "club_price" : "15.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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