Kuratowski's theorem states that every nonplanar graph contains either the utility
graph 
or the pentatope graph 
as a homeomorphic subgraph. 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's 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.House
of Graphs. Kuratowski Graphs. K5
and Utility Graph K3,3.Referenced on Wolfram|Alpha
Kuratowski GraphCite this as:
Weisstein, Eric W. "Kuratowski Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KuratowskiGraph.html