False Disproof

Like many theorem, there would be people who would exploit to prove the theorem wrong. Four Color Theorem has had multiple false proofs and misrepresentation in its long history. These self-assertions come from many people simply one major assumption usu on the wholey comes from graph makers. much(prenominal) map as the one below cant use this theorem:

This graph cant use the theorem because both(prenominal) the A blocks represent the same country. In this map, not all countries are contiguous so this would not work because the theorem clear states that it has to be contiguous. Like many theorem there are confinement to what a region is considered and the theorem usually clear states the restriction. Many new(prenominal) assumptions would re-word the theorem, for example if a region only has to be coloured differently from regions it touches directly, not regions touching regions that it touches. If this were the restriction, planar graphs would require helter-skelter large numbers of vividnesss (NationMaster). This would be true solely the theorem clearly states that the region has to be adjacent so this assumption is false. Theorem only holds true, if two regions is considered adjacent if they share an infinite length of boundary.



Touching a single boundary point wouldnt be considered adjacency and any assumption that doesnt clearly understand this would be false because the theorem clearly states this.
There is a easy way to determine the maximum number of color for a certain step to the fore. If it is a closed (orientable or non-orientable) surface with positive genus, the maximum p colors depend on the surfaces Euler characteristic χ according to the formula as:

* This is the degree function of p.

If the surface is orientable the formula can be given in terms of the genus of a surface, g:

* This is the floor function of p.

With these equation, it is easy to optimize the graph with as fewer colors as possible so it would be easier to bear witness and understand....If you want to get a full essay, order it on our website: Orderessay



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