The vertices of the polygon are then 3-colored in such a way that every triangle has all three colors.
For his accomplishment Kempe was elected a Fellow of the Royal Society and later President of the London Mathematical Society.
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Guthrie’s brother passed on the question to his mathematics teacher Augustus de Morgan at University College, who mentioned it in a letter to William Hamilton in 1852.
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The cavity method has played and is playing a major role in the solution of optimization problems like the K-satisfiability and the graph coloring in present days.