The Fritsch graph is the planar graph on nine vertices illustrated above that tangles the Kempe chains in Kempe's coloring algorithm and thus provides an example of how the supposed proof of the four-color theorem by Kempe (1879) fails.
The Fritsch graph is implemented in the Wolfram Language as GraphData["FritschGraph"].
The Fritsch graph and Soifer graph provide smallest possible counterexamples for Kempe's false proof. In fact, removing a particular edge from the Fritsch graph gives the Soifer graph.
The Fritsch graph is isomorphic to the skeleton of the triaugmented triangular prism.
