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2009 How false is Kempe's proof of the Four Color Theorem? Part II
Gethner Ellen, Nao Takano, Bopanna Kallichanda, Alexander Mentis, Sarah Braudrick, Sumeet Chawla, Andrew Clune, Rachel Drummond, Panagiota Evans, William Roche
Involve 2(3): 249-265 (2009). DOI: 10.2140/involve.2009.2.249


We continue the investigation of A. B. Kempe’s flawed proof of the Four Color Theorem from a computational and historical point of view. Kempe’s “proof” gives rise to an algorithmic method of coloring plane graphs that sometimes yields a proper vertex coloring requiring four or fewer colors. We investigate a recursive version of Kempe’s method and a modified version based on the work of I. Kittell. Then we empirically analyze the performance of the implementations on a variety of historically motivated benchmark graphs and explore the usefulness of simple randomization in four-coloring small plane graphs. We end with a list of open questions and future work.


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Gethner Ellen. Nao Takano. Bopanna Kallichanda. Alexander Mentis. Sarah Braudrick. Sumeet Chawla. Andrew Clune. Rachel Drummond. Panagiota Evans. William Roche. "How false is Kempe's proof of the Four Color Theorem? Part II." Involve 2 (3) 249 - 265, 2009.


Received: 23 November 2008; Accepted: 23 November 2008; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1177.05038
MathSciNet: MR2551124
Digital Object Identifier: 10.2140/involve.2009.2.249

Primary: 05C15, 68R10, 90C35

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.2 • No. 3 • 2009
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