# Modern Graph Theory

• Béla Bollobás
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 184)

1. Front Matter
Pages i-xiv
2. Béla Bollobás
Pages 1-37
3. Béla Bollobás
Pages 39-66
4. Béla Bollobás
Pages 67-102
5. Béla Bollobás
Pages 103-144
6. Béla Bollobás
Pages 145-179
7. Béla Bollobás
Pages 181-214
8. Béla Bollobás
Pages 215-252
9. Béla Bollobás
Pages 253-293
10. Béla Bollobás
Pages 295-334
11. Béla Bollobás
Pages 335-378
12. Back Matter
Pages 379-397

### Introduction

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.

### Keywords

algebra computer computer science graph graph theory graphs Matching mathematics network networks polynomial Ramsey theory

#### Authors and affiliations

• Béla Bollobás
• 1
• 2
1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA
2. 2.Trinity CollegeUniversity of CambridgeCambridgeUK

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0619-4