Tag Archives: Four color

Four color theorem: Cahit spiral chains (step two)


Now the application is able to find all spiral chains of a graph. I still need to: Implement the Cahit coloring algorithm using the spiral chains Add some additional features to the Java application Modify the settings to color the … Continue reading

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Four color theorem: other representations of maps


Here are some new representation of graphs: Thanks to: http://mathoverflow.net/questions/63861/representations-of-regular-maps-four-color-theorem http://www.geogebra.org/forum/viewtopic.php?f=2&t=21841

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Four color theorem: representations of maps


For the scope of the four color problem and without lack of generality, maps can be represented in different ways. This is generally done to have a different perspective on the problem. For example, the graph-theoretic representation of maps has … Continue reading

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Counting maps


I’ve posted this question on mathoverflow. Is there a formula to count how many different topological regular maps can be created with n faces (on a sphere)? For “regular” I intend maps in which the boundaries form a 3-regular planar … Continue reading

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Four color theorem: recap


Recap (some facts about maps and coloring): All regular maps (3-regular planar graphs) can be topologically transformed (represented) as circular or rectangular maps In searching for a solution of the four color problem, it is possible to exclude maps with … Continue reading

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Are these different colorings?


UPDATE (18/Apr/2011) The nunber of proper colorings (not considering permutations of colors) can be count using the “Chromatic polynomial” and dividing the result by 4! (factorial that counts the permutations). But, the chromatic polynomial is only known for few types … Continue reading

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T1 was already known


The theorem I proved in T1 was already known. It was found by Kempe back in 1879 in terms of graph theory (see http://en.wikipedia.org/wiki/Four_color_theorem: “Kempe also showed correctly that G can have no vertex of degree 4″). Only 132 years later … Continue reading

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