Graph Theory

ISBN-10: 3642142788
ISBN-13: 9783642142789
Edition: 4th 2010
Authors: Reinhard Diestel
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Book details

Edition: 4th
Copyright year: 2010
Publisher: Springer
Publication date: 7/19/2010
Binding: Paperback
Pages: 410
Size: 6.25" wide x 9.50" long x 1.25" tall
Weight: 1.848
Language: English

Preface
The Basics
Graphs*
The degree of a vertex*
Paths and cycles*
Connectivity*
Trees and forests*
Bipartite graphs*
Contraction and minors*
Euler tours*
Some linear algebra
Other notions of graphs
Exercises
Notes
Matching Covering and Packing
Matching in bipartite graphs*
Matching in general graphs(*)
Packing and covering
Tree-packing and arboricity
Path covers
Exercises
Notes
Connectivity
2-Connected graphs and subgraphs*
The structure of 3-connected graphs(*)
Menger's theorem*
Mader's theorem
Linking pairs of vertices(*)
Exercises
Notes
Planar Graphs
Topological prerequisites*
Plane graphs*
Drawings
Planar graphs: Kuratowski's theorem*
Algebraic planarity criteria
Plane duality
Exercises
Notes
Colouring
Colouring maps and planar graphs*
Colouring vertices*
Colouring edges*
List colouring
Perfect graphs
Exercises
Notes
Flows
Circulations(*)
Plows in networks*
Group-valued flows
k-Flows for small k
Flow-colouring duality
Tutte's flow conjectures
Exercises
Notes
Extremal Graph Theory
Subgraphs*
Minors(*)
Hadwiger's conjecture*
Szemer�di's regularity lemma
Applying the regularity lemma
Exercises
Notes
Infinite Graphs
Basic notions, facts and techniques*
Paths, trees, and ends(*)
Homogeneous and universal graphs*
Connectivity and matching
Graphs with ends: the topological viewpoint
Recursive structures
Exercises
Notes
Ramsey Theory for Graphs
Ramsey's original theorems*
Ramsey numbers(*)
Induced Ramsey theorems
Ramsey properties and connectivity(*)
Exercises
Notes
Hamilton Cycles
Sufficient conditions*
Hamilton cycles and degree sequences*
Hamilton cycles in the square of a graph
Exercises
Notes
Random Graphs
The notion of a random graph*
The probabilistic method*
Properties of almost all graphs*
Threshold functions and second moments
Exercises
Notes
Minors, Trees and WQO
Well-quasi-ordering*
The graph minor theorem for trees*
Tree-decompositions
Tree-width and forbidden minors
The graph minor theorem(*)
Exercises
Notes
Infinite sets
Surfaces
Hints for all the exercises
Index
Symbol index

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