Colorful Mathematics: Part II
4. The Hamilton connection
Any plane graph, whether it is 3-valent or not, that has a Hamiltonian circuit can be so colored with 4 colors . Unfortunately, there are infinitely many graphs that have no Hamiltonian circuit so this approach to trying to prove the four-color theorem did not prove fruitful. However, there is an interesting story here.
In the next column, we will continue our discussion of coloring problems and their applications.
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