Tag Archives: Hamilton

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

Posted in Uncategorized | Tagged , , , , , , , , , , , , , | 5 Comments

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

Posted in Uncategorized | Tagged , , , , , , , , , , , , , | Leave a comment

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

Posted in Uncategorized | Tagged , , , , , , , , , , , , , | Leave a comment