| Preface 1 The Basics 1.1 Graphs 1.2 The degree of a vertex 1.3 Paths and cycles 1.4 Connectivity 1.5 Trees and forests 1.6 Bipartite graphs 1.7 Contraction and minors 1.8 Euler tours 1.9 Some linear algebra 1.10 Other notions of graphs Exercises Notes 2 Matching, Covering and Packing 2.1 Matching in bipartite graphs 2.2 Matching in general graphs 2.3 Packing and covering 2.4 Tree-packing and arboricity 2.5 Path covers Exercises Notes 3 Connectivity 3.1 2-Connected graphs and subgraphs.. 3.2 The structure of 3-connected graphs 3.3 Menger's theorem 3.4 Mader's theorem 3.5 Linking pairs of vertices Exercises Notes 4 Planar Graphs 4.1 Topological prerequisites 4.2 Plane graphs 4.3 Drawings 4.4 Planar graphs: Kuratowski's theorem. 4.5 Algebraic planarity criteria 4.6 Plane duality Exercises Notes 5 Colouring 5.1 Colouring maps and planar graphs 5.2 Colouring vertices 5.3 Colouring edges 5.4 List colouring 5.5 Perfect graphs Exercises Notes 6 Flows 6.1 Circulations 6.2 Flows in networks 6.3 Group-valued flows 6.4 k-Flows for small k 6.5 Flow-colouring duality 6.6 Tutte's flow conjectures Exercises Notes 7 Extremal Graph Theory 8 Infinite Graphs 9 Ramsey Theory for Graphs 10 Hamilton Cycles 11 Random Grapnhs 12 Mionors Trees and WQO |
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