Book:Reinhard Diestel/Graph Theory/Fourth Edition

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

Subject Matter

 * Graph Theory

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