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.
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).
I learned graph theory from the inexpensive duo of Introduction to Graph Theory by Richard J. Trudeau and Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield and Gerhard Ringel. Both are excellent despite their age and cover all the basics. They aren't the most comprehensive of sources and they do have some age issues if you want an up to date presentation, but for the basics they can't be beat.
There are lots of good recommendations here, but if cost isn't an issue, the most comprehensive text on the subject to date is Graph Theory And Its Applications by Jonathan Gross and Jay Yellen. This massive, beautifully written and illustrated tome covers just about everything you could possibly want to know about graph theory, including applications to computer science and combinatorics, as well as the best short introduction to topological graph theory you'll find anywhere. If you can afford it, I would heartily recommend it. Seriously.
Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield and Gerhard Ringel.
I used this book to teach a course this semester, the students liked it and it is a very good book indeed. The book includes number of quasiindependent topics; each introduce a brach of graph theory. It avoids tecchnicalities at all costs. I would include in the book basic results in algebraic graph theory, say Kirchhoff's theorem, I would expand the chapter on algorithms, but the book is VERY GOOD anyway.
I enjoyed Alan Tucker's Applied Combinatorics. It's split into two sections:
- Graph Theory
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.
Here is Vadim Lozin's graph theory course. (Available for free from university of Warwick website )
It starts from scratch and most of theorems are prooved. I think it's pretty clear with many content.
It's not a book, but i hope it can help you.
Graph Theory: Modeling, Applications, and Algorithms by Geir Agnarsson and Raymond Greenlaw is a really good book. see this discussion for reference.