The article mentions at the end the problem of coloring graphs on other surfaces. It's worth noting, it's known, for every surface, what the maximum chromatic number is of a graph on that surface: https://en.wikipedia.org/wiki/Heawood_conjecture

The odd thing about the Ringel-Youngs theorem is that proving the upper bound on the chromatic number is, with the exception of the case of the sphere (i.e., planar graphs, i.e. the four color theorem), not that hard. For the sphere, the lower bound is easy and the upper bound is hard; for other surfaces, the upper bound is easy and the hard part, if any, is the lower bound! (And then also the Klein bottle is an exception and requires only 6 colors instead of 7, so that one also requires a separate more-involved upper bound argument, but nothing on the scale of the four-color theorem...)