I've got an exercise that I've been battling for 5 hours to solve. There is a picture of the graph below. I am sure that I can't find a K5 as a minor since every vertex has 3 edges leaving. I tried so long to find a K3,3 minor and failed. What is the correct approach? I also strongly believe that it is not planar graph.
Delete the edges $\{EG\}$ and $\{FH\}$. Then you can do the following: