圖論

內(nèi)容概要

Almost two decades have passed since the appearance of those graph theory texts that still set the agenda for most introductory courses taught today. The canon created by those books has helped to identify some main fields of study and research, and will doubtless continue to influence the development of the discipline for some time to come. 　　Yet much has happened in those 20 years, in graph theory no less than elsewhere: deep new theorems have been found, seemingly disparate methods and results have become interrelated, entire new branches have arisen. To name just a few such developments, one may think of how the new notion of list colouring has bridged the gulf between invuriants such as average degree and chromatic number, how probabilistic methods and the regularity lemma have pervaded extremai graph theory and Ramsey theory, or how the entirely new field of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph problems.

書籍目錄

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, 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 subgraphs..   3.2 The structure of 3-connected graphs   3.3 Menger's theorem   3.4 Mader's theorem   3.5 Linking pairs of vertices  Exercises  Notes4 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  Notes5 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  Notes6 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  Notes7 Extremal Graph Theory8 Infinite Graphs9 Ramsey Theory for Graphs10 Hamilton Cycles11 Random Grapnhs12 Mionors Trees and WQO

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