# Tag Archives: Kenneth Appel

## Four color theorem: what next?

The algorithm I use to color graphs works pretty well … BUT: Sometimes (very rarely) it gets into an infinite loop where also random Kempe color switches (around the entire graph) do NOT work. The good is, if I reprocess … Continue reading

## 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

## 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

## 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

## 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

## Four color theorem: slow motion maps

Here is a video that shows the nature of rectangular and circular maps. All maps concerning the four color theorem (“regular maps” | “planar graphs without loops”) can be topologically transformed into rectangular and circular maps.

## Four color theorem: which one is the correct graph?

Wikipedia: “In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, every planar graph is four-colorable.” … Continue reading