What does /sci/ think about graph theory?

very beautiful theory in its own right that happens to have myriad applications

it's a meme

Very useful.

its for queers

It's a useful meme for queers.

M E M E
E
M
E

Pictures are for babies.

>>7686796
One of my relatives published a famous theorem in the subject, but I'm not too familiar with it yet

total spoopyness.

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One of my favourite areas of mathematics.

>>7686796
What's a modern graph theory exactly? I only can remember one nontrivial theorem in graph theory course, it's one of Pontryagin's.

>>7688474
Graph theory is largely interesting because of how trivial it is, while still having tons of applications.

>>7688474
graph polynomials is a big area of study, topological graph theory studies which graphs have which kind of embeddings on different surfaces, some other people use crazy linear algebra to solve coloring problems, and finally there is the study of graph algorithms and optimization.

there's actually more to modern graph theory than this, but I wouldn't be a good person to get into that.

>>7688488
you didn't have a very good graph theory course did you?

yes there are lots of trivial results about graphs because they are very simple objects. Students learn and master these in a few weeks and then prove non trivial results.

It's edgy as fuck.

orbifolds am i right?

>>7688551
You have a point.

>>7688500

Maybe he's talking about the trivial parts (stuff you'd learn in an intro discrete course) of it having lots of applications. Or at least I hope that's what he means, as graph theory is certainly not trivial.

I certainly have noticed that though. The parts of it that I would ever use outside of academia are mostly the very basic parts, although I suppose that's true for almost every single branch of mathematics...

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>>7688491

There also seems to be a lot of research on certain classes of graphs, such as various kinds of perfect graphs or X-free graphs, where X is some kind of induced subgraph(Like K1,3), usually small, since those can often have nice properties, especially with respect to algorithms. I guess other specific kinds of classes of graphs too, since you can often get polynomial time algorithms for problems which are NP-hard on general graphs, although I guess that's venturing more into the CS side of graph theory, although honestly I see a lot of mathematicians researching that too, just as I see computer scientists doing non-algorithmic graph theory. There's a pretty big overlap between CS and Math stuff in graph theory.

>>7687455

Most graph theory doesn't actually involve many pictures, as you usually just resort to symbols for everything like in most math. Unless it's for a concrete example/counterexample, I guess. Or an illustration to show a concept, but none of the proofs or actual work will have pictures.

Are there any students (math,cs, whatever) in grad school studying graph theory on /sci/?

>>7688840
cool answer

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>>7686796
>computer science
I'm so sorry.

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>>7691280
But isn't that a part of algorithms in general? Also, you won't be posting that picture on /sci/ for much longer.

I just finished my "Hello World" program, and I'm working on a Java program to hack your 4chan account.

Enjoy posting that picture while you still can.

>>7691280

Is it the same person who posts this picture in every thread that's even slightly related to CS? (despite the fact that graph theory is a field of math, and CS was barely mentioned in the thread)

>>7692629
desu I'm a CS major and I just do it for lulz and to pre-empt the other guy who posts the meme just in case he's serious.

>>7692771
That's why he does it too.

>>7691280
Closed minded fuck, group theory has intimate links with graph theory.

>>7690739

Doing a phd on graph

>>7693833
phd on graph? sounds pretty cool man. Where do you school and what area in GT specifically? Any algorithmic stuff?

I'm taking a graph-theory class with this mofo next sem: he works on some object called the abelian sandpile which is fucking cool

http://www.math.cmu.edu/~wes/index.html

>>7693833

What area(s) of it are you doing research in?

>>7693850
>>7693879

I am in France. I mostly do some stuff on structural graph theory (like colouring but not only). Typical question is probably something like (not that I work on this, thank god) : https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Hajnal_conjecture

>>7693887

Is most of your research on a specific subclass of graphs, since you're doing structural graph theory?

>>7693891

Not at all. I know that some people have their specfic class of graph (perfect, planar etc) but I don't. I'm just starting though so it might happen, but I am doubtful

Boring.

>>7686796
if you took a class on graph theory but have not learned topology, consider yourself having not learned graph theory.

>>7692771

CS majors don't even learn graph theory.

>>>/g/tfo

>>7694098

Topological graph theory is only a subfield of graph theory anyway. And we had some basic topology as part of my graph theory.

Really, it depends what you mean by not learned graph theory - that's true in the case that you've only learned some of it, but that would still be the case even if you had studied topology previously.

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>>7693922

Can you be more specific about what you studied/are studying then? I'm considering doing a masters and studying graph theory once I finish my bachelors, but I'm not sure if I want to get into it. I noticed a lot of results when I was looking at papers were for certain subclasses of graphs and such, but I think I enjoy results on general graphs a lot more, even if those results aren't usually as tight. I guess in terms of applications some of those results might be pretty useful... but how often would those subclasses of graphs even come up in practice, outside of super niche situations? Although I guess if people keep finding nice results on all these certain classes of graphs, then eventually when you have a problem it will be more likely that your model will fit into a certain class that has nice results.

I'm primarily interested in the topic more just for its own sake.. but I'd also like to be able to apply some of what I've known once I'm done, instead of just spending time/money learning for fun, although I wouldn't want to study an area of the field that I did not enjoy that much, even if it was really useful.

>>7692771
Thank you for your indispensable service, Anon.

>>7694125
>CS majors don't even learn graph theory.
shit tier uni kek

>>7694806

It is very natural in graph to study subclasses to try to solve the whole problem. Some people use this to have a lot of paper on useless stuff, but honestly, if you don't go into a PHD and only study graph for your master, you shouldn't see these types of result.

As far as being useful, if you go in the algorithmic part or in the combinatorial optimisation part, you can do a lot of interesting things.

>>7694098

>muh graph on surfaces

>>7694885
In some sense he's right though. A CS class on graph theory will always be more superficial than a math class on graph theory. CS majors don't have the mathematical prerequisite knowledge to go deeper into the topic, e.g. they don't know topology, abstract algebra or stochastic processes.

>>7695006
The best results in graphs don't use any of the topic you mentioned though. I will admit that some discrete probability is necessary, but I hope all CS student have this knowledge.

>>7688551
>>7688625
Speaking of triviality

>>7695006

We used group theory (mostly permutation groups) with regard to graph automorphisms (among other applications and types of groups inb4 someone brings up Cayley's theorem to say that that's all groups) a fair bit in one of my CS courses, so I wouldn't say that. I've seen group theory crop up in a few other CS courses as well. We also studied topological graph theory more than we did in the math course I took in graph theory, which surprised me,

Not to mention that when you talk about going deeper, there are many other ways to delve deeper into graph theory than just what you talked about.

The prereqs for the CS graph course and the Math graph course are the same though, as well, since CS requires 2 discrete courses here.