Tag Archives: graph coloring

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: Cahit spiral chains


Hi, I’ve found some time to implement the first version of Cahit Spiral Chains algorithm. I still need to: Find all spiral chains of a given graph and not only one (changing the starting point) I need to implement the … Continue reading

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Four color theorem: videos


Four videos for the four color theorem. music coloring algorithm slow motion maps java application features

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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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