简介
From the reviews:"B閘a Bollob醩 introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and group... more 籹. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletinof the London Mathematical Society#1 ?less
目录
Table of Contents 8
Foreword 6
Chapter 1. Characterizations and classifications of biconnected graphs 10
Chapter 2. Line graphs and their chromatic polynomials 24
Chapter 3. Large graphs with given degree and diameter III 32
Chapter 4. Distinguishing vertices of random graphs 42
Chapter 5. The trail number of a graph 60
Chapter 6. Message graphs 70
Chapter 7. Sets of graph colourings 74
Chapter 8. On Hadwiger\u2019s number and the stability number 80
Chapter 9. A depth-first-search characterization of planarity 84
Chapter 10. Graph-theoretical model of social organization 90
Chapter 11. Odd cycles of specified length in non-bipartite graphs 98
Chapter 12. Simplicial decompositions: Some new aspects and applications 110
Chapter 13. Achievement and avoidance games for graphs 120
Chapter 14. Embedding incomplete latin rectangles 130
Chapter 15. Edge-colouring regular bipartite graphs 148
Chapter 16. Some colouring problems and their complexity 168
Chapter 17. A Hamiltonian game 180
Chapter 18. Finite Ramsey theory and strongly regular graphs 188
Chapter 19. The connectivities of a graph and its complement 200
Annals of Discrete Mathematics 212
Foreword 6
Chapter 1. Characterizations and classifications of biconnected graphs 10
Chapter 2. Line graphs and their chromatic polynomials 24
Chapter 3. Large graphs with given degree and diameter III 32
Chapter 4. Distinguishing vertices of random graphs 42
Chapter 5. The trail number of a graph 60
Chapter 6. Message graphs 70
Chapter 7. Sets of graph colourings 74
Chapter 8. On Hadwiger\u2019s number and the stability number 80
Chapter 9. A depth-first-search characterization of planarity 84
Chapter 10. Graph-theoretical model of social organization 90
Chapter 11. Odd cycles of specified length in non-bipartite graphs 98
Chapter 12. Simplicial decompositions: Some new aspects and applications 110
Chapter 13. Achievement and avoidance games for graphs 120
Chapter 14. Embedding incomplete latin rectangles 130
Chapter 15. Edge-colouring regular bipartite graphs 148
Chapter 16. Some colouring problems and their complexity 168
Chapter 17. A Hamiltonian game 180
Chapter 18. Finite Ramsey theory and strongly regular graphs 188
Chapter 19. The connectivities of a graph and its complement 200
Annals of Discrete Mathematics 212
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