I recall that a torus requires 7. However, stranger surfaces require more colors: for example, divisions of the … Applications Of Mathematics In Everyday Life. For any given map, we can construct its dual graph as follows. Given a map drawn on the plane or the surface of a sphere, the famous four color theorem asserts that it is always possible to properly color the regions of the map such that no two adjacent regions are assigned the same color, using at most four distinct colors . I tried finding real life applications for the Four Color Theorem (except for coloring maps) but couldn't find anything useful and well illustrated. Four colors can easily be shown to be required. J. Ferro (pers. From Wikipedia: “The four color theorem, on vertex coloring of planar graphs, is equivalent to the statement that every bridgeless 3-regular planar graph is of class one (Tait 1880). This statement is now known to be true, due to the … Continue reading → comm., Nov. 8, 2005) has debunked a number of purported "short" proofs of the four-color theorem. We cover the four color theorem controversy, discuss the proof of the four color theorem and explain computer-assisted proofs in mathematics. Two regions are considered to be adjacent if they share a common boundary that is not a corner (a point shared by three or more regions). But a proof that 4 was sufficient was elusive. CCS Discrete II Professor: Padraic Bartlett Lecture 4: Graph Theory and the Four-Color Theorem Week 4 UCSB 2015 Through the rest of this class, we’re going to refer frequently to things called graphs! I recall that a torus requires 7. The four-colour map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the regions of the map so that no two adjacent regions have the same colour. C++ Four color theorem implementation using greedy coloring (Welsh-Powell algorithm) - okaydemir/4-color-theorem But a proof that 4 was sufficient was elusive. Since the plane can be mapped to a sphere, the four color theorem applies to a sphere as well, essentially saying that any map on a globe can be colored with at most four colors. I need to apply the four colors theorem in a polygonal shape in a way that I do not need to choose manually each color to put in each region. Martin Gardner (1975) played an April Fool's joke by asserting that the McGregor map consisting of 110 regions required five colors and constitutes a counterexample to the four-color theorem. The Four-Color Theorem: History, Topological Foundations, and Idea of Proof Graphs, Colourings and the Four-Colour Theorem Other sites with applications to color maps or related apps: