What are good books to learn graph theory?

Question

What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.

Answer 1

Try Bondy and Murty, Graph Theory. The previous version, Graph Theory with Applications, is available online.

Answer 2

Doug West, Introduction to Graph Theory. Rigorous but readable, proof based rather than simply descriptive, but the proofs are explanatory rather than simply justification of truth (by any arbitrary means). Even so may not be the best total beginner's book.

Answer 3

Diestel's Graph Theory (which has a "free preview" online) is presented as a graduate textbook, but it does not really have any prerequisites.

It goes quite deep in some parts, and includes material (such as the chapter on the graph minor theorem) that you won't find in other textbooks. Some proofs have a sort of "how would someone ever think of that?" feel, but this may have been remedied in the fourth edition (I have the third).

Answer 4

The best introduction I could recommend for truly beginners is not a whole book on graph theory but A Walk Through Combinatorics, from Miklos Bona it has a large part of the book devoted to graph theory, from the very basics up to some intro to Ramsey theory

Answer 5

You might find Graph Algorithms / Shimon Even interesting. Although it might probably hard to obtain.

Edit: You can get some of the chapters here.

Answer 6

I enjoyed Alan Tucker's Applied Combinatorics. It's split into two sections:

• Graph Theory
• Combinatorics

The first half covers things like coloring theorems, cycles, and all that stuff. The second half is all about generating functions, counting sets, etc.

I found the book to be pretty readable. There are a lot of problems to work, which was nice.

Answer 7

I have used Diestel's Graph Theory book mainly, but I found extremely helpful video lectures by professor L. Sunil Chandran from IISc Bangalore (here and here).