Show that the following graph is planar or not.

Given graph

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?

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

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

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  • $\begingroup$ Stupid me, I never tried to get a K3,3 :(. Thank you @HEKTO $\endgroup$ – ilirosmanaj Jan 28 '18 at 9:50

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