The Kuratowski's theorem says, that a graph is planar if, and only if it doesn't contain a subgraph that is a subdivision of or . We are now using instead the more general theorem of Klaus Wagner and look for minors of and . On the application below you can see the Petersen graph.
Try to find the and minor in the Petersen graph.
-You can merge vertices that are connected by edges by moving them together and left-clicking them.
-You can use the rubber-tool to delete vertices and edges.
-To restore the original version press the refresh-button on the right top.
-You can rearrange the vertices of the and and try to overlap them with the Petersen graph.

If you have problems merging two vertices, try to wait a bit after clicking a vertex. Also check if the vertices are connected through an edge. You can also try to switch to the html 5 version.
You will have to reset the application to solve the problem. Therefore just reload the page.