Introduction to Graph Theory [5 ed.] 9780273728894
In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool
1,273 176 5MB
English Pages 184 [193] Year 2010
Table of contents :
Cover
Contents
Preface
Introduction
Chapter 1 - Definitions and Examples
1.1 - Definitions
1.2 - Examples
1.3 - Variations on a theme
1.4 - Three puzzles
Chapter 2 - Paths and Cycles
2.1 - Connectivity
2.2 - Eulerian graphs and digraphs
2.3 - Hamiltonian graphs and digraphs
2.4 - Applications
Chapter 3 - Trees
3.1 - Properties of trees
3.2 - Counting trees
3.3 - More applications
Chapter 4 - Planarity
4.1 - Planar graphs
4.2 - Euler's formula
4.3 - Dual graphs
4.4 - Graphs on other surfaces
Chapter 5 - Colouring Graphs
5.1 - Colouring vertices
5.2 - Chromatic polynomials
5.3 - Colouring maps
5.4 - The four-color theorem
5.5 - Colouring edges
Chapter 6 - Matching, Marriage, and Menger's Theorem
6.1 - Hall's 'marriage' theorem
6.2 - Menger's theorem
6.3 - Network flows
Chapter 7 - Matroids
7.1 - Introduction to matroids
7.2 - Examples of matroids
7.3 - Matroids and graphs
Appendix 1: Algorithms
Appendix 2: Table of numbers
List of symbols
Bibliography
Solutions to Selected Exercises
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index
Cover
Contents
Preface
Introduction
Chapter 1 - Definitions and Examples
1.1 - Definitions
1.2 - Examples
1.3 - Variations on a theme
1.4 - Three puzzles
Chapter 2 - Paths and Cycles
2.1 - Connectivity
2.2 - Eulerian graphs and digraphs
2.3 - Hamiltonian graphs and digraphs
2.4 - Applications
Chapter 3 - Trees
3.1 - Properties of trees
3.2 - Counting trees
3.3 - More applications
Chapter 4 - Planarity
4.1 - Planar graphs
4.2 - Euler's formula
4.3 - Dual graphs
4.4 - Graphs on other surfaces
Chapter 5 - Colouring Graphs
5.1 - Colouring vertices
5.2 - Chromatic polynomials
5.3 - Colouring maps
5.4 - The four-color theorem
5.5 - Colouring edges
Chapter 6 - Matching, Marriage, and Menger's Theorem
6.1 - Hall's 'marriage' theorem
6.2 - Menger's theorem
6.3 - Network flows
Chapter 7 - Matroids
7.1 - Introduction to matroids
7.2 - Examples of matroids
7.3 - Matroids and graphs
Appendix 1: Algorithms
Appendix 2: Table of numbers
List of symbols
Bibliography
Solutions to Selected Exercises
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index
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