Ramsey's Theorem for graphs

Given any n, there's a smallest number R(n) such that, for any coloring of the edges of the complete graph on R(n) vertices, there's a monochromatic copy of the complete graph on n vertices. These numbers are devilishly hard to find: so far only up to R(4) are known. What about infinite graphs?

Video rendered in Python, using mostly manim (by 3b1b) and other libraries, some are my own.