In mathematics , the four color theorem , or the four color map theorem , states that , given any separation of a plane into contiguous regions , producing a figure called a map , no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color .
Intuitively , the four color theorem can be stated as ` given any separation of a plane into contiguous regions , called a map , the regions can be colored using at most four colors so that no two regions which are adjacent have the same color ' .