In the mathematical field of

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, the Kittell graph is a

planar graph In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...

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 Sir Alfred Bray Kempe FRS (6 July 1849 – 21 April 1922) was a mathematician best known for his work on linkages and the four colour theorem. Biography Kempe was the son of the Rector of St James's Church, Piccadilly, the Rev. John Edwar ...

's flawed proof of the

four-color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions shar ...

. Simpler counterexamples include the Errera graph and Poussin graph (both published earlier than Kittell) and the Fritsch graph and Soifer graph.

References

Individual graphs Planar graphs {{graph-stub