Graph Theory

Graduate Texts in Mathematics #244

by U.S.R. Murty

Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics – computer science, combinatorial optimization, and operations research in particular – but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.



The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided tohelp the reader master the techniques and reinforce their grasp of the material.



A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.

Genres: Mathematics, Science, Computer Science, Academic, Textbooks, Reference

675 pages, Hardcover

First published August 14, 2007

Reviews

[Dan Boeriu · Rating 5 out of 5]

This is the best graph theory book at graduate level. It's unitary, it has fluent, articulate proofs which makes it easy to read. The authors have a great pedagogical sense on how to present a math concept. The book underlines proof techniques and makes a point on how to clearly prove something. Nothing pretentious, just good old-fashioned mathematics at work. The book presents quite a few new(er) results in the field and has comprehensive recommendations at the end of each chapters.
This edition is a lot more comprehensive than the first edition and it is more difficult.

[Andrew · Rating 4 out of 5]

The best graph theory book I have seen thus far, and the only one I have seen where the subject feels connected rather than a collection of scattered results around a common theme. There are several choices the authors made that I believe help with this overall feeling of unity to the subject:
1. Introducing Ford-Fulkerson early and recalling it with future instantiations of the theorem (i.e. Menger's theorem, Edmonds' branching theorem, etc.).
2. The highly useful insets that show how the theory of combinatorics is largely built around methods and strategies, rather than algebraic theory.
3. Discussing chromatic polynomial, flow polynomial, and Tutte polynomials, which identify common patterns for graph invariants.

[Ayush Bhat · Rating 5 out of 5]

This book represents a very good introduction to what is a fascinating branch of mathematics. The topics included represent all the "big" areas in graph theory. The discourse is just enough to whet the appetite for more advanced study, while remaining very accessible.

[Francisco Nunes · Rating 5 out of 5]

Truly great book, one of the best Mathematics books I’ve used. It contains very clear explanations and has a lot of visual material so you can understand the text better.

I’m so happy we used this book in our Graph Theory course at Aarhus University.