Four Colour Theorem

366 Words2 Pages
The Four Colour Theorem Essay The four colour conjecture was proposed by Francis Guthrie, a student at University College in London where he studied under a professor named DeMorgan. After graduation, his brother became a pupil of DeMorgan. Francis told his brother about a conjecture he had been trying to prove involving the colouration of maps. He instructed his brother to ask the professor for assistance. Unfortunately, DeMorgan was puzzled by the conjecture. Throughout the years, DeMorgan asked mathematicians about the conjecture. Eventually, a mathematician by the name of Alfred Bay Kempe announced that he had discovered a proof of the Four Colour Conjecture. Kempe had his proof published to the American Journal of Mathematics. To prove the Theorem, he used a method known as the Method of Kempe Chains which states: “If we have a map in which every region is coloured red, green, blue or yellow except one, say X. If this final region X is not surrounded by regions of all four colours there is a colour left for X. Hence suppose that regions of all four colours surround X. If X is surrounded by regions A, B, C, D in order, coloured red, yellow, green and blue then there are two cases to consider. (i) There is no chain of adjacent regions from A to C alternately coloured red and green. (ii) There is a chain of adjacent regions from A to C alternately coloured red and green. If (i) holds there is no problem. Change A to green, and then interchange the colour of the red/green regions in the chain joining A. Since C is not in the chain it remains green and there is now no red region adjacent to X. Colour X red. If (ii) holds then there can be no chain of yellow/blue adjacent regions from B to D. [It could not cross the chain of red/green regions.] Hence property (i) holds for B and D and we change colours as above.” In the year 1976 the Four Colour Conjecture

More about Four Colour Theorem

Open Document