```Date: Mar 7, 2014 8:00 AM
Author: Peter Percival
Subject: Re: 4 colors problem

Peter Percival wrote:> Arturo Magidin wrote:>>> The theorem is **NOT** about "patterns". The theorem does **NOT** say>> that there is an algorithm for producing a coloring, as you seem to>> think. The theorem says that **GIVEN** a map, a coloring exists *for>> that map*.>> May I ask if there is a practical algorithm?  Clearly there is an> algorithm: colour the given (finite) map in all possible ways with four> or fewer colours, examine each colouring in turn until an admissible one> is found.  The theorem ensures that one will be found.  But that would> be quite impractical.To answer my own question: "Since the proving of the theorem, efficient algorithms have been found for 4-coloring maps requiring only O(n^2) time, where n is the number of vertices." is from http://en.wikipedia.org/wiki/Four_colour_map_problem.-- Madam Life's a piece in bloom,Death goes dogging everywhere:She's the tenant of the room,He's the ruffian on the stair.
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