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 invariants 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.
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 2.1. Matching in bipartite graphs 2.2. Matching in general graphs 2.3. Path covers Exercises Notes 3.Connectivity4.Palanar Graphs5.Colouring6.Flows7.Substructures in Dense Graphs8.Substructures in Sparse Graphs9.Ramsey Theory for Graphs10.Hamilton Cycles11.Random Graphs12.Minors,Threes,and WQOHints for all the exercisesIndexSymbol index
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