Book:Reinhard Diestel/Graph Theory

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
 * 2.1. Matching in bipartite graphs
 * 2.2. Matching in general graphs
 * 2.3. 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. Edge-disjoint spanning trees
 * 3.6. Paths between given 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. Substructures in Dense Graphs
 * 7.1. Subgraphs
 * 7.2. Szemeredi's regularity lemma
 * 7.3. Applying the regularity lemma
 * Exercises
 * Notes


 * 8. Substructures in Sparse Graphs
 * 8.1. Topological minors
 * 8.2. Minors
 * 8.3. Hadwiger's conjecture
 * 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. Simple 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 minor theorem for trees
 * 12.3. Tree-decompositions
 * 12.4. Tree-width and forbidden minors
 * 12.5. The minor theorem
 * Exercises
 * Notes


 * Index
 * Symbol index