I am a rising senior in a small liberal arts college, and I was wondering if anyone could suggest me good graduate schools for graph theory. My only exposure to graph theory has been the intro graph theory course at my school, so I clearly do not know much about the different varieties of graph theory, but I was wondering if anyone could shed some light on the graduate schools which provide research focus on any of the varieties of graph theory.
closed as offtopic by Ricardo Andrade, Boris Bukh, YCor, Steven Landsburg, Bjørn KjosHanssen Jun 23 '15 at 3:54
This question appears to be offtopic. The users who voted to close gave this specific reason:
 "This question does not appear to be about research level mathematics within the scope defined in the help center." – Ricardo Andrade, Boris Bukh, YCor, Steven Landsburg, Bjørn KjosHanssen

1$\begingroup$ This question should probably be tagged as Community Wiki $\endgroup$ – Yemon Choi Jun 6 '13 at 22:59

1$\begingroup$ Are there any geographical preferences? This would be good to know. $\endgroup$ – The User Jun 6 '13 at 23:25

$\begingroup$ There are rankings for U.S. grad schools in "discrete math and combinatorics". Not the same as graph theory, but it's a decent place to start. (Take it with a grain of salt, though.) gradschools.usnews.rankingsandreviews.com/… $\endgroup$ – Sam Nolen Jun 6 '13 at 23:41

16$\begingroup$ I know I should keep to comments that only relate to the question, but my recommendation is to go to the best place you get in and not just apply to places that have what you think you want to do. Most people (especially if you only have a small exposure) end up changing their minds after the first year of grad school. You'll want good people in all sorts of fields if this happens. $\endgroup$ – Matt Jun 7 '13 at 1:53

$\begingroup$ Thanks, @Matt. Yeah, I think I'm one of those people who have little exposure, and I'm trying to balance my applications as to what I want to study and also where there is wide breadth. Thanks for the advice. $\endgroup$ – Sunny Jun 7 '13 at 17:59
The University of Waterloo has an entire Faculty of Mathematics, consisting of several departments: Pure Math, Applied Math, Combinatorics & Optimization, Statistics, Operations Research, and (at least when I went there) Computer Science.
Anyway, the Department of C&O has several people that work on graph theory, as you can see here: http://math.uwaterloo.ca/combinatoricsandoptimization/research/areas#graphtheory

3$\begingroup$ And if you are willing to go to Canada, Simon Fraser University has a pretty good graph theory group as well. $\endgroup$ – Casteels Jun 7 '13 at 0:31
First of all, let me point out that I am not a graph theorist.
I have been told by a graph theorist that UCSD has very strong faculty specifically in graph theory. It also seems to me that Rutgers has some very strong combinatorialists and graph theorists. Ultimately you should decide on a place based on who you would like and are likely to work with.
EDIT: A small remark regarding Matt comment. I've seen two types of people in graduate school. Those that arrive not knowing what they want to do and those that arrive because they knew already what they want to do and with whom. People in the second category typically have already done research in the field and start working on some questions right away. People in the first category take more time, take some course, and find out what they like. Of course there are exceptions to everything.

$\begingroup$ I'd definitely like to second that Rutgers recommendation. Great school for combinatorics and graph theory! $\endgroup$ – Vidit Nanda Jun 23 '15 at 1:29
I was a part of the Budapest Semesters in Math way back in 2007, and many of the others who studied in that program went on to phds in graph theory (I was the black sheep, going for algebraic topology instead). Several went to CEU in Budapest, and loved it. You can work with any professor in the city, and as you can imagine there are some very powerful graph theorists there (Laszlo Lovasz springs to mind). One or two also ended up at USC (that's South Carolina, not southern California) and worked with Szemeredi. If I was going for graph theory I think those two would be high on my list. Another interesting idea is University of Chicago to work with Laszlo Babai. He's technically computer science but has supervised mathematicians before.
By the way, I second Waterloo and Rutgers

$\begingroup$ Thanks, David. I also went to Budapest, and CEU does sound like a great idea. Location wise I would prefer to be in the United states, even though I have not given much thought on this particular issue. Thanks for the advice; I will look up these programs. $\endgroup$ – Sunny Jun 7 '13 at 17:59

$\begingroup$ Just be aware that CEU only gives funding for 3 years, and most americans need longer than that because they enter grad school without a masters degree. So at the end you might end up paying your rent out of pocket, but it seems worth it to me if you love Budapest $\endgroup$ – David White Jun 7 '13 at 20:19
Another option would be Northeast university, which has a ph.d. program on network science (basically applied graph theory). Barabasi and Vespigniani are faculty there, and if you have had little exposure, you may want to consider a more practical approach
Here's my (incomplete) list of recommendations based on my current knowledge of graph theory research.
General: Rutgers, UCSD, Tel Aviv, Waterloo, McGill, Princeton, Yale, Eötvös Loránd University, Rényi Institute, Emory University, Queen Mary University of London, Warwick University, Simon Frasier University, Charles University in Prague, University of Hamburg.
Algebraic Graph Theory: Waterloo, University of Western Australia, Tilburg University, CWI Amsterdam, QMUL, Imperial College London, Tohoku University, Delaware, Clemson, Michigan Technological University, Wyoming.