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The Graph Theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. It has has a surprising number of applications: in physics, biology, chemistry, social, commerce, and computer science. In this book we view one part of Graph theory called route problems. The route problem contains a lot of diffente problems. For example the Travelling Salesman Problem is the problem of finding a tour that visits each cityexactly once and that minimises the total distance travelled. Many tour has been founded thank to TPS for example The Sweden tour is 24.978 cities problem which was solved in May 2004
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