FACTOID # 4: Just 1% of the houses in Nevada were built before 1939.

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Encyclopedia > Heawood conjecture

The Heawood conjecture in graph theory was an expected formula to give the correct upper bound for the number of colors which are sufficient for graph coloring on a surface of a given genus. It was mostly proved in 1968 by Gerhard Ringel and J. W. T. Youngs. The non-orientable case of the Klein bottle proved exceptional. In mathematics and computer science, graph theory studies the properties of graphs. ... In logic, the words necessary and sufficient describe relations that hold between propositions or states of affairs, if one is conditional on the other. ... A 3-coloring suits this graph, but fewer colors would result in adjacent verticies of the same color. ... In mathematics, the genus has few different meanings Topology The genus of a connected, oriented surface is an integer representing the maximum number of cuttings along closed simple curves without rendering the resultant manifold disconnected. ... The Klein bottle immersed in three-dimensional space. ...

P.J. Heawood conjectured that for a graph G of orientable genus g, This article or section should be merged with Orientable manifold. ...

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where χ(G) is the chromatic number of G, and is the floor function. A 3_coloring suits this graph, but fewer colors would result in adjacent verticies of the same color. ... In mathematics, the floor function is the function defined as follows: for a real number x, floor(x) is the largest integer less than or equal to x. ...

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 The four colour theorem (1703 words) Charles Peirce in the USA attempted to prove the Conjecture in the 1860's and he was to retain a lifelong interest in the problem. Heawood was to work throughout his life on map colouring, work which spanned nearly 60 years. Reynolds increased it to 27 in 1926, Winn to 35 in 1940, Ore and Stemple to 39 in 1970 and Mayer to 95 in 1976.
 PlanetMath: four-color conjecture (240 words) The four-color conjecture was a long-standing problem posed by Francis Guthrie to his professor Augustus De Morgan in 1852, while coloring a map of England. The conjecture states that every map on a plane or a sphere can be colored using only four colors such that no two adjacent countries are assigned the same color. This conjecture equivalent to the statement that chromatic number of every planar graph is no more than four.
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