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I am looking for a graph theory and combinatorics text for someone with limited background in linear algebra(I am not yet into college math;I have only read a bit of group theory and completed single variable calculus).I did study some combinatorics while preparing for the mathematical olympiads though.

I am not new to proofs but I am looking for a short text(perhaps, less than 300 pages) written rigorously with good but not exceptionally hard problems,aimed perhaps at undergraduates.I want the focus of the book to be graph theory though.


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up vote 4 down vote accepted

Combinatorics Through Guided Discovery (free!) is one of my favorite books. If you're looking for good problems, use this book. The entire book is made up of problems!

Combinatorics and Graph Theory by John M. Harris is also a good book.

Edit: I just realized you want a book focused on graph theory. The second book is probably better for that purpose, although the first contains some graph theory as well.

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+1 for Combinatorics and Graph Theory – Snowball Oct 24 '12 at 14:55

I suggest you to read "Ore O. - Graphs and their uses" or "W.D. Wallis - A Beginner's Guide to Graph Theory".

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You could start with László Lovász & Kati Vesztergombi, Discrete Mathematics, which is available in ps format here and in pdf format here; it’s only about $140$ pages, it’s free, and it does both some graph theory and some general combinatorics. However, the graph theory in it is very limited, being presented largely as an application of the combinatorial ideas.

For more on the graph theory, you might try this text by Bender & Williamson; it too is freely available. It introduces both general combinatorics and basic graph theory and goes a bit further into both than the Lovász and Vesztergombi. It’s a little longer than you specified, but most of the excess is appendices and solutions.

At the very least you can use either or both as auxiliary texts, since they’re free.

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László Lovász & Kati Vesztergombi's, Discrete Mathematics has easier problems than I am accustomed to. :( – user43081 Oct 24 '12 at 13:24
@Chris: Having taught from those notes, I knew that this was a possibility, but I thought them worth mentioning anyway; a lot of my undergraduates found it pretty rough going. – Brian M. Scott Oct 24 '12 at 13:29

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