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 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 Edward K ...
'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 sha ...
.
Simpler counterexamples include the
Errera graph
In the mathematical field of graph theory, the Errera graph is a graph with 17 vertices and 45 edges. Alfred Errera published it in 1921 as a counterexample to Kempe's erroneous proof of the four color theorem; it was named after Errera by .
Pro ...
and
Poussin graph (both published earlier than Kittell) and the
Fritsch graph and
Soifer graph.
References
Individual graphs
Planar graphs
{{graph-stub