In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. https://en.wikipedia.org/wiki/Four_color_theorem
What if the map was restricted to a pixelated image, i.e. a grid of colored squares? Would a much simpler proof suffice? Has such a proof been published?
EDIT 1: On a pixilated map, at most 4 regions can meet at a point. There is no theoretical limit on a continuous map. So maybe some simplification is possible?
EDIT 2: On a finite pixilated map, there is at most a finite number of regions. The maximum is equal to the number of pixels. There is no maximum on even a finite continuous map.