Book:Reinhard Diestel/Graph Theory/Fourth Edition

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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 Szemer├ędi'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