Examples of the Four Color Theorem, which states that no more than four colors are required to color in any map so that no two adjacent regions share the same color
Made by me in Photoshop
Good luck with that. It took 124 years to prove.
An intuitive deduction makes me think it’s 8.
0-dimensions require 1 color. 1-dimension requires 2 colors. 2-dimensions require 4 colors.
A quick Googling didn’t provide an answer.
There’s no bounds for 3 dimensions. The 4 color theorem is a result on planar graphs (graphs that can be drawn in 2 dimensions without an edge crossing) but in three dimensions every graph can be drawn without edge crossings, including graphs where everything is next to everything else, so there isn’t a bound.
Neat.