File:Poussin_graph_tangled_Kempe_chains.svg
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![File:Poussin graph tangled Kempe chains.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Poussin_graph_tangled_Kempe_chains.svg/534px-Poussin_graph_tangled_Kempe_chains.svg.png)
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Summary
DescriptionPoussin graph tangled Kempe chains.svg |
English: Tangled Kempe chains in the Poussin graph. The map shown has regions whose adjacencies form the Poussin graph. All but one of the regions (the outer region) have been colored, and must be recolored in order to color the whole map. This map and its coloring provides a counterexample to Kempe's erroneous proof of the four color theorem. In this case, because the blue-yellow and blue-green Kempe chains (shown as dashed lines) are connected, Kempe's proof would try to swap the colors on the red-yellow chain on the left, and the red-green chain on the right, freeing the red color for the outer face. But because the blue-yellow and blue-green chains cross each other, Kempe's recoloring would cause the uppermost yellow and green regions to both become red, producing an invalid coloring. |
Date | |
Source | Own work |
Author | David Eppstein |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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25 March 2017
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 03:31, 26 March 2017 | ![]() | 534 × 535 (6 KB) | David Eppstein | recenter |
03:27, 26 March 2017 | ![]() | 534 × 535 (6 KB) | David Eppstein | Missed some bits of the red chain | |
03:20, 26 March 2017 | ![]() | 534 × 535 (6 KB) | David Eppstein | User created page with UploadWizard |
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Width | 534.416px |
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Height | 535.064px |