Tag Archives: Alfred Bray Kempe

Four color theorem: about edges selection


For the decomposition of a graph representing a map, I’m trying to use different algorithms to select the edge to remove. The question is: When you have multiple valid choices, which is the best edge to select … if any? Some basic … Continue reading

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Four color theorem: almost there?


Here there are some results that came out from the study of Kempe chains/cycles (of edges) in Tait coloring of a 3-regular planar graph. Next is shown an image with a summary of the ideas behind this approach. I didn’t have the time to … Continue reading

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Four color theorem: back to the basics


Finally I bought two books about the four color theorem: “Four Colors Suffice: How the Map Problem Was Solved” by Robin Wilson e Ian Stewart; and the “The Four-Color Theorem: History, Topological Foundations, and Idea of Proof” by Rudolf Fritsch and Gerda Fritsch. I’am in … 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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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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