It is equivalent to the n=5 and n=6 cases of the Hadwiger Conjecture, and may be viewed as the genus zero case of the Heawood Conjecture, which gives upper bounds on chromatic numbers for graphs that can be embedded in various topological surfaces.  
It is equivalent to the n=5 and n=6 cases of the Hadwiger Conjecture, and may be viewed as the genus zero case of the Heawood Conjecture, which gives upper bounds on chromatic numbers for graphs that can be embedded in various topological surfaces.  In 1890, Heawood pointed out the error in Alfred Kempe's proposed proof of it by using an example with 18 regions.  In 1976, Wolfgang Haken and Kenneth Appel proved it by combining Kempe's idea with a controversial use of computer analysis. FTP, what is this theorem stating that only a certain number of hues are needed to illustrate a map so that no two neighboring regions are shaded the same?
It is equivalent to the n=5 and n=6 cases of the Hadwiger Conjecture, and may be viewed as the genus zero case of the Heawood Conjecture, which gives upper bounds on chromatic numbers for graphs that can be embedded in various topological surfaces.  
Four-Color Map Theorem (accept equivalents)