# Four-Color Maps

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For 66 years, research on the four-color theorem was dominated by Tait's Hamiltonian graph conjecture: any cubic polyhedral graph has a Hamiltonian cycle. In a graph, cubic means that every vertex is incident with exactly three edges. Any planar graph can be made cubic by drawing a small circle around any vertex with valence greater than three and eliminating the original vertex. Tutte, in 1946, found the first counterexample to Tait's conjecture.

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Contributed by: Ed Pegg Jr (March 2011)

Open content licensed under CC BY-NC-SA

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"Four-Color Maps"

http://demonstrations.wolfram.com/FourColorMaps/

Wolfram Demonstrations Project

Published: March 7 2011