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Graph Theory [Bondy] - mklabgr - 08-17-2026
Graph Theory
Authors: J. A. (Adrian) Bondy and U. S. R. Murty
Publication: 2008
Publisher: Springer London
Series:Graduate Texts in Mathematics, Vol. 244
Length: about 650 pages
ISBN: 978-1-84628-969-9
Graph Theory by Bondy and Murty is a comprehensive and rigorous introduction to one of the central areas of discrete mathematics. Intended primarily for advanced undergraduate and beginning graduate students in mathematics and computer science, the book develops graph theory systematically while maintaining the intuitive and visual character that makes the subject attractive. It begins with fundamental ideas about graphs, subgraphs, connectedness and trees, then develops major themes including network flows, connectivity, planar graphs, the Four-Colour Problem, independent sets and cliques, vertex and edge colouring, matchings, Hamiltonian cycles, coverings and packings, electrical networks, and integer flows.
A particularly strong feature is the emphasis on mathematical reasoning rather than simply collecting theorems. Bondy and Murty repeatedly introduce proof techniques, demonstrate how they work in important results, and then reinforce them through a substantial collection of exercises of varying difficulty. The presentation also connects pure graph theory with applications in computer science, combinatorial optimization, operations research and communication networks. Algorithmic ideas and computational complexity therefore appear naturally alongside the theoretical mathematics. This makes the book valuable not only for learning what the important results of graph theory are, but also for learning how graph theorists approach and solve problems.
The text goes beyond a conventional introductory textbook. Its later and more advanced sections introduce readers to research-level ideas, and the authors explicitly discuss challenging and unsolved problems. This gives the book an unusual progression: a student can use selected sections for a first serious course, while a more experienced reader can continue deeper into individual chapters as preparation for research. The Mathematical Association of America described the 2008 book as a substantial reworking and expansion of Bondy and Murty's earlier classic Graph Theory with Applications, noting its breadth in both theory and applications.
Key takeaways
- Broad and rigorous: Covers most of the major areas of classical graph theory while reaching into advanced topics and open problems.
- Proof-oriented: Particularly valuable for developing techniques of mathematical proof and combinatorial problem solving.
- Theory meets algorithms: Builds connections among pure mathematics, algorithms, optimization, networks and computer science.
- Best suited to serious study: It is more demanding than a casual introduction, but an excellent choice for advanced undergraduates, graduate students, self-study, or someone preparing to pursue research in graph theory.
Goodreads book page
Springer book page