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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Diestel, Reinhard. Graph Theory. : Springer, ©2012 |

Material Type: | Document |

Document Type: | Book, Computer File |

All Authors / Contributors: |
Reinhard Diestel |

ISBN: | 9783642142796 3642142796 |

OCLC Number: | 794328663 |

Description: | 1 online resource (452 pages) |

Contents: | Title; Preface; About the second edition; About the third edition; About the fourth edition; Contents; 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 subgraphs3.2 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 k6.5 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 theorems9.4 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 theoremExercises; Notes; Appendix A: Infinite sets; Appendix B: Surfaces; Hints for all theExercises; Hints for Chapter 1; Hints for Chapter 2; Hints for Chapter 3; Hints for Chapter 4; Hints for Chapter 5; Hints for Chapter 6; Hints for Chapter 7; Hints for Chapter 8; Hints for Chapter 9; Hints for Chapter 10; Hints for Chapter 11; Hints for Chapter 12; Index; Symbol Index. |

### Abstract:

HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study.€Rezension"Deep, clear, wonderful. This is a serious book about the.

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