单词 | Four-Color Theorem |
释义 | Four-Color TheoremThe four-color theorem states that any map in a Plane can be colored using four-colors in such a way that regionssharing a common boundary (other than a single point) do not share the same color. This problem is sometimes also calledGuthrie's Problem after F. Guthrie, who first conjectured the theorem in 1853. The Conjecture was thencommunicated to de Morgan and thence into the general community. In 1878, Cayley Fallacious proofs were given independently by Kempe (1879) and Tait Finally, Appel and Haken (1977) announced a computer-assisted proof that four colors were Sufficient. However, becausepart of the proof consisted of an exhaustive analysis of many discrete cases by a computer, some mathematicians do notaccept it. However, no flaws have yet been found, so the proof appears valid. A potentially independent proof has recentlybeen constructed by N. Robertson, D. P. Sanders, P. D. Seymour, and R. Thomas. Martin Gardner (1975) played an April Fool's joke by (incorrectly) claiming that the map of 110 regions illustrated belowrequires five colors and constitutes a counterexample to the four-color theorem. ![]()
Appel, K. and Haken, W. ``Every Planar Map is Four-Colorable, I and II.'' Illinois J. Math. 21, 429-567, 1977. Appel, K. and Haken, W. ``The Solution of the Four-Color Map Problem.'' Sci. Amer. 237, 108-121, 1977. Appel, K. and Haken, W. Every Planar Map is Four-Colorable. Providence, RI: Amer. Math. Soc., 1989. Barnette, D. Map Coloring, Polyhedra, and the Four-Color Problem. Providence, RI: Math. Assoc. Amer., 1983. Birkhoff, G. D. ``The Reducibility of Maps.'' Amer. Math. J. 35, 114-128, 1913. Chartrand, G. ``The Four Color Problem.'' §9.3 in Introductory Graph Theory. New York: Dover, pp. 209-215, 1985. Coxeter, H. S. M. ``The Four-Color Map Problem, 1840-1890.'' Math. Teach., Apr. 1959. Franklin, P. The Four-Color Problem. New York: Scripta Mathematica, Yeshiva College, 1941. Gardner, M. ``Mathematical Games: The Celebrated Four-Color Map Problem of Topology.'' Sci. Amer. 203, 218-222, Sep. 1960. Gardner, M. ``The Four-Color Map Theorem.'' Ch. 10 in Martin Gardner's New Mathematical Diversions from Scientific American. New York: Simon and Schuster, pp. 113-123, 1966. Gardner, M. ``Mathematical Games: Six Sensational Discoveries that Somehow or Another have Escaped Public Attention.'' Sci. Amer. 232, 127-131, Apr. 1975. Gardner, M. ``Mathematical Games: On Tessellating the Plane with Convex Polygons.'' Sci. Amer. 232, 112-117, Jul. 1975. Kempe, A. B. ``On the Geographical Problem of Four-Colors.'' Amer. J. Math. 2, 193-200, 1879. Kraitchik, M. §8.4.2 in Mathematical Recreations. New York: W. W. Norton, p. 211, 1942. Ore, Ø. The Four-Color Problem. New York: Academic Press, 1967. Pappas, T. ``The Four-Color Map Problem: Topology Turns the Tables on Map Coloring.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 152-153, 1989. Robertson, N.; Sanders, D. P.; and Thomas, R. ``The Four-Color Theorem.'' http://www.math.gatech.edu/~thomas/FC/fourcolor.html. Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, 1986. Tait, P. G. ``Note on a Theorem in Geometry of Position.'' Trans. Roy. Soc. Edinburgh 29, 657-660, 1880. |
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