HPS391H1 Chapter Notes - Chapter 1: Frederick Guthrie, Pentagon, Francis Guthrie
29 Apr 2016
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Four colors suffice: how the map problem was solved by robin. Suppose one wants to assign colours to the countries on a map in such a way that no two neighbouring countries - with a common boundary consisting of more than just isolated points -receive the same colour. The first recorded reference to the problem is in a letter from augustus de morgan to sir william rowan hamilton written in 1852. De morgan had learned of the problem from one of his students, frederick guthrie, who had learned of the problem from his brother, francis guthrie. In 1879 kempe attempted to show that four colours were always sufficient by an inductive argument that started with euler"s polyhedral formula. Consider a non- trivial (connected) planar map with e boundary lines or edges, v vertices, or points where three or more boundary lines meet, and f countries or faces - including one infinite face.
