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Fritsch Graph

المؤلف:  Fritsch, R. and Fritsch, G

المصدر:  The Four-Color Theorem. New York: Springer-Verlag, 1998.

الجزء والصفحة:  ...

27-3-2022

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Fritsch Graph

 

The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof of the four-color theorem fails.

The Fritsch graph and Soifer graph provide smallest possible counterexamples for Kempe's false proof.

The Fritsch graph is isomorphic to the skeleton of the triaugmented triangular prism.

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REFERENCES

Fritsch, R. and Fritsch, G. The Four-Color Theorem. New York: Springer-Verlag, 1998.

Gethner, E. and Springer, W. M. II. "How False Is Kempe's Proof of the Four-Color Theorem?" Congr. Numer. 164, 159-175, 2003.

Kempe, A. B. "On the Geographical Problem of Four-Colors." Amer. J. Math. 2, 193-200, 1879.