# Book:Reinhard Diestel/Graph Theory/Fourth Edition

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## Reinhard Diestel:

## Reinhard Diestel: *Graph Theory (4th Edition)*

Published $\text {2010}$, **Springer**.

This book is volume 173 of the **Graduate Texts in Mathematics** series.

### Subject Matter

### Contents

- 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
- 7.1 Subgraphs*
- 7.2 Minors(*)
- 7.3 Hadwiger's conjecture*
- 7.4 Szemerédi's regularity lemma
- 7.5 Applying the regularity lemma
- Exercises
- Notes

- 8. Infinite Graphs
- 8.1 Basic notions, facts and techniques*
- 8.2 Paths, trees, and ends(*)
- 8.3 Homogeneous and universal graphs*
- 8.4 Connectivity and matching
- 8.5 Graphs with ends: the topological viewpoint
- 8.6 Recursive structures
- Exercises
- Notes

- 9. Ramsey Theory for Graphs
- 9.1 Ramsey's original theorems*
- 9.2 Ramsey numbers(*)
- 9.3 Induced Ramsey theorems
- 9.4 Ramsey properties and connectivity(*)
- Exercises
- Notes

- 10. Hamilton Cycles
- 10.1 Sufficient conditions*
- 10.2 Hamilton cycles and degree sequences*
- 10.3 Hamilton cycles in the square of a graph
- Exercises
- Notes

- 11. Random Graphs
- 11.1 The notion of a random graph*
- 11.2 The probabilistic method*
- 11.3 Properties of almost all graphs*
- 11.4 Threshold functions and second moments
- Exercises
- Notes

- 12. Minors, Trees and WQO
- 12.1 Well-quasi-ordering*
- 12.2 The graph minor theorem for trees*
- 12.3 Tree-decompositions
- 12.4 Tree-width and forbidden minors
- 12.5 The graph minor theorem(*)
- Exercises
- Notes

- A. Infinite sets

- B. Surfaces

- Hints for all the exercises
- Index
- Symbol index