The four color theorem is a theorem of mathematics . It says that in any plane surface with regions in it ( people think of them as maps ) , the regions can be colored with no more than four colors . 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 .