All Map Coloring and Topological Graph Theory

This group gathers theorems about coloring maps and drawing graphs on surfaces, the part of topology that meets graph theory. Its subject is how the regions of a plane or another surface can be colored so that neighbors differ, and how the shape of a surface limits the colorings and embeddings that are possible. It holds results in the line of the four color theorem, which says that no more than four colors are required to color the regions of any map and which was the first major theorem proved with the help of a computer, together with their relatives for maps on other surfaces. Theorems about graphs that matter mainly for their combinatorial structure, with no appeal to surfaces, belong with Combinatorics and Graph Theory instead.