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. 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.
