how can we calculate ramsey numbers

Question

thomas5267 · Answer

I don't think it can be easily calculated. http://en.wikipedia.org/wiki/Ramsey%27s_theorem "Erdős asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5, 5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6, 6). In that case, he believes, we should attempt to destroy the aliens."

anonymous · Answer

but if we want to calculate r(3,3) then what is its method? i know the answer is 6...but how it comes thats what i want to know

zzr0ck3r · Answer

Well for that particular problem, it can be stated another way. 

In any party of six people either at least three of them are (pairwise) mutual strangers or at least three of them are (pairwise) mutual acquaintances.

If you need help proving this let me know. Hint: Show that in any simple graph G (wlog) there is either a triangle in G or there is a triangle in its compliment.

zzr0ck3r · Answer

And just to let you know how hard this can be, there are Ramsey numbers that exists that for all of human existence there will never be a computer fast enough to compute them by counting cases.