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.

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.