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. ...
, 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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