{"product_id":"the-hamiltonian-circuit-algorithm-ashay-dharwadker-9781466381377","title":"The Hamiltonian Circuit Algorithm","description":"We present a new polynomial-time algorithm for finding Hamiltonian circuits in graphs. It is shown that the algorithm always finds a Hamiltonian circuit in graphs that have at least three vertices and minimum degree at least half the total number of vertices. In the process, we also obtain a constructive proof of Dirac's famous theorem of 1952, for the first time. The algorithm finds a Hamiltonian circuit (respectively, tour) in all known examples of graphs that have a Hamiltonian circuit (respectively, tour). In view of the importance of the P versus NP question, we ask: does there exist a graph that has a Hamiltonian circuit (respectively, tour) but for which this algorithm cannot find a Hamiltonian circuit (respectively, tour)? The algorithm is implemented in C++ and the program is demonstrated with several examples.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Ashay Dharwadker\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 146638137X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781466381377\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 34\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.23lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.50w x 0.09d","brand":"Ashay Dharwadker","offers":[{"title":"Paperback","offer_id":48217377702143,"sku":"9781466381377","price":15.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_9ccea3ed-a554-49c8-9f24-f3e7f98c6618.jpg?v=1771996839","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-hamiltonian-circuit-algorithm-ashay-dharwadker-9781466381377","provider":"WR Book House","version":"1.0","type":"link"}