The Kuratowski reduction theorem states that very nonplanar graph contains either the
utility graph 
or the pentatope graph 
as a graph
minor. The graphs 
and 
are therefore known as Kuratowski graphs (Duke and Haggard 1972, Harary et al.
1973) or Kuratowski subgraphs.
Kuratowski Graph
See also
Kuratowski Reduction Theorem, Pentatope GraphExplore with Wolfram|Alpha
References
Duke, R. A.; and Haggard, G. "The Genus of Subgraphs of
."
Israel J. Math. 11, 452-455, 1972.Harary, F.; Kainen,
P. C.; Schwenk, A. J.; and White, A. T. "A Maximal Toroidal Graph
Which Is Not a Triangulation." Math. Scand. 33, 108-112, 1973.Referenced on Wolfram|Alpha
Kuratowski GraphCite this as:
Weisstein, Eric W. "Kuratowski Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KuratowskiGraph.html