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Phase Transitions in Combinatorial Optimization …

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ArXiv:cond-mat/0602129v1 [ ] 6 Feb 2006Phase Transitions inCombinatorial OptimizationProblemsAlexander K. Hartmann and Martin WeigtWILEY-VCH Verlag GmbH & Co. KGaAFebruary 3, 20083 Introduction to graphsThe next three sections give a short introduction to graph theory and graph algorithms. Thefirst one deals with the basic definitions and concepts, and introduces some graph second one is dedicated to some fundamental graph algorithms. In the third one, we willdiscuss random graphs, which will be of fundamental importance throughout this us begin by mentioning some books related to graph theory. All of them go well beyondeverything we will need concerning graphs: Gary Chartrand,Introductory graph theory, Dover Publ.

26 3 Introduction to graphs Figure 3.1 shows the river Pregel, Königsbergwas situated on both sides and bothislands. The seven bridges are also shown.

  Phases, Transition, Optimization, Phase transitions in combinatorial optimization, Combinatorial

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