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Phase Transitions in Combinatorial Optimization …

ArXiv:cond-mat/0602129v1 [ ] 6 Feb 2006 Phase 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.

3.1 Basic concepts and graph problems 29 In the above definitions for undirected graphs, edges have no orientation. This is different for directed graphs …

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