Graph Theory - Amazing Fact About Planar vs Non-Planar Graphs

A planar graph is one that can be drawn in a plane without any edges crossing. The surprising fact behind Kuratowski’s Theorem (and Wagner’s Theorem) is that all non-planar graphs “contain” K5 or K3,3! 😲

Kuratowski’s Theorem:
A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 or K3,3.

Wagner’s Theorem
A finite graph is planar if and only if its minors do not include K5 or K3,3.

[jayraldbasan]

Hi! Might i ask what program/software are you using in making the graphs?