# Kittell graph

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In the mathematical field of [graph theory](/source/Graph_theory), the **Kittell graph** is a [planar graph](/source/Planar_graph) with 23 vertices and 63 edges. Its unique planar embedding has 42 triangular faces.[1] The Kittell graph is named after Irving Kittell, who used it as a counterexample to [Alfred Kempe](/source/Alfred_Kempe)'s flawed proof of the [four-color theorem](/source/Four-color_theorem).[2] Simpler counterexamples include the [Errera graph](/source/Errera_graph) and [Poussin graph](/source/Poussin_graph) (both published earlier than Kittell) and the [Fritsch graph](/source/Fritsch_graph) and [Soifer graph](/source/Soifer_graph).

## References

1. Kittell, Irving (1935), ["A group of operations on a partially colored map"](https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-41/issue-6/A-group-of-operations-on-a-partially-colored-map/bams/1183498239.pdf), *[Bulletin of the American Mathematical Society](/source/Bulletin_of_the_American_Mathematical_Society)*. **41** (6): 407–413, [doi:10.1090/S0002-9904-1935-06104-X](https://doi.org/10.1090/S0002-9904-1935-06104-X). MR 1563103

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