Excluding maps that can be colored with 2 or 3 colors, how many different four coloring exist for a given regular map?
Naturally, two identical maps have to be regarded as differently colored if the same coloring cannot be obtained by swapping colors inside one of the two maps. It is also intended that the two maps used the same set of four colors.
Is there a paper on this? Someone has already studied this?
UPDATE: If someone is interested I opened the same question on mathoverflow: here is the link to the same question: http://mathoverflow.net/questions/61225/how-many-different-colorings-excluding-exchanges-exist-for-a-given-map-graph