I am working with a professor on a research paper and we believe this graph is a counter example to our work, but we need to be sure. We cannot determine if this graph is planar and we need to for our research.
If you are able to see a subdivision of a K5 or a K3,3 as a subgraph of the image, then it is non planar, but we cannot find one, but we also cannot make it planar… please help.
https://i.sstatic.net/FNPTL.png
Best Answer
Merge all the vertices that have not been labelled into one vertex, call it $5$ then $1,2,3,4,5$ will be a graph isomorphic to $K_5$.