{"product_id":"the-clique-algorithm-ashay-dharwadker-9781466391215","title":"The Clique Algorithm","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Ashay Dharwadker\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1466391219\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781466391215\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Createspace Independent Publishing Platform\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/02\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 48\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.30lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.50w x 0.12d","brand":"Ashay Dharwadker","offers":[{"title":"Paperback","offer_id":48217377800447,"sku":"9781466391215","price":15.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_4f6849b0-76e9-4826-8fdf-3dd6fe112156.jpg?v=1771996839","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-clique-algorithm-ashay-dharwadker-9781466391215","provider":"WR Book House","version":"1.0","type":"link"}