Wagner's theorem states that a graph is planar iff it does not contain or as a graph minor.
Wagner's Theorem
See also
Kuratowski's Theorem, Robertson-Seymour TheoremExplore with Wolfram|Alpha
References
Bondy, J. A. and Murty, U. S. R. Graph Theory. Berlin: Springer-Verlag, p. 269, 2008.Kuratowski, C. "Sur le problème des courbes gauches en topologie." Fund. Math. 15, 217-283, 1930.Wagner, K. "Über eine Eigenschaft der ebenen Komplexe." Math. Ann. 114, 570-590, 1937.Cite this as:
Weisstein, Eric W. "Wagner's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WagnersTheorem.html