# Show that graph is planar or not?

Show that the following graph is planar or not.

My first assumption is that this graph is not planar, but could not find a reasonable prove (except saying that I tried drawing it in different ways in plane, but couldn't).

We know that a graph is non-planar if it contains either K5 or K3,3 as minors. I tried getting I subdivision of this graph (by contracting some edges), but failed to get a K5 (which I think should be possible).

Any ideas anyone?

• There are several characterisations of planar graphs. Check one of them. – Raphael Jan 27 '18 at 20:49

Contract edges $(C,D)$ and $(G,H)$ - and you'll get $K_{3,3}$.