This theorem is the m-equals-one case of the empire problem.
This theorem is the m-equals-one case of the empire problem. P. G. Tait introduced snarks in his attempt to prove this theorem. This theorem extended Heawood's theorem to the case of genus zero. This theorem would be strengthened by the Hadwiger conjecture, whose k-equals-5 case would eliminate one possible minor. One incorrect proof of this theorem made use of Kempe chains, which nonetheless reduce the problem to the case of minimum degree 5. This theorem's proof was completed in 1976 at the University of Illinois by Appel and Haken, who checked 1,936 specific cases by computer. For 10 points, name this result that gives an upper bound on the number of colors required by planar graphs.
This theorem is the m-equals-one case of the empire problem.
four color map theorem &lt;Thompson&gt;