In the mathematical field of

graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

, the Kittell graph is a

planar graph In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cro ...

with 23 vertices and 63 edges. Its unique planar embedding has 42 triangular faces. The Kittell graph is named after Irving Kittell, who used it as a counterexample to Alfred Kempe's flawed proof of the four-color theorem. Simpler counterexamples include the Errera graph and

Poussin graph In graph theory, the Poussin graph is a planar graph with 15 vertices and 39 edges. It is named after Charles Jean de la Vallée-Poussin. History In 1879, Alfred Kempe published a proof of the four color theorem, one of the big conjectures in g ...

(both published earlier than Kittell) and the

Fritsch graph The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular prism by attaching equilateral square pyramids to each of its three square faces. The same ...

and

Soifer graph Soifer is a surname. Notable people with the surname include: * Alexander Soifer (born 1948), Russian-born American mathematician and mathematics author *Aviam Soifer Aviam Soifer (born 1948) is an American legal scholar who worked on high-profi ...

References

Individual graphs Planar graphs {{graph-stub