From Gonthier (2008): "Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors." Gonthier, Georges (2008), "Formal Proof—The Four-Color Theorem"(PDF), Notices of the American Mathematical Society, 55 (11): 1382–1393, MR2463991, archived(PDF) from the original on 2011-08-05
Steinberg, Richard (1993), "The state of the three color problem", in Gimbel, John; Kennedy, John W.; Quintas, Louis V. (eds.), Quo Vadis, Graph Theory?, Annals of Discrete Mathematics, vol. 55, Amsterdam: North-Holland, pp. 211–248, doi:10.1016/S0167-5060(08)70391-1, ISBN978-0-444-89441-0, MR1217995
From Gonthier (2008): "Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors." Gonthier, Georges (2008), "Formal Proof—The Four-Color Theorem"(PDF), Notices of the American Mathematical Society, 55 (11): 1382–1393, MR2463991, archived(PDF) from the original on 2011-08-05
Steinberg, Richard (1993), "The state of the three color problem", in Gimbel, John; Kennedy, John W.; Quintas, Louis V. (eds.), Quo Vadis, Graph Theory?, Annals of Discrete Mathematics, vol. 55, Amsterdam: North-Holland, pp. 211–248, doi:10.1016/S0167-5060(08)70391-1, ISBN978-0-444-89441-0, MR1217995
From Gonthier (2008): "Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors." Gonthier, Georges (2008), "Formal Proof—The Four-Color Theorem"(PDF), Notices of the American Mathematical Society, 55 (11): 1382–1393, MR2463991, archived(PDF) from the original on 2011-08-05