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Graph Theory - KIT

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Graph TheoryLecture by Prof. Dr. Maria AxenovichLecture notes by M onika Csik os, Daniel Hoske and Torsten Ueckerdt1Contents1 Introduction32 Notations33 Preliminaries44 Matchings135 Connectivity176 Planar graphs227 Colorings278 Extremal Graph theory309 Ramsey theory3410 Flows3811 Random graphs4012 Hamiltonian cycles4213 Kuratowski s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other coloring results . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preparation for Tur an s theorem.

3 Preliminaries De nition 3.1. A graph Gis an ordered pair (V;E), where V is a nite set and graph, G E V 2 is a set of pairs of elements in V. The set V is called the set of vertices and Eis called the set of edges of G. vertex, edge The edge e= fu;vg2

  Theory, Graph, Graph theory

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Introduction These notes include major de nitions, theorems, and proofs for the graph theory course given by Prof. Maria Axenovich at KIT during the winter term 2019/20.

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