I'm having trouble with the two graphs below. Graph appears like it will have a $K_5$, however, I can't connect the vertices properly. How do these graphs have a $K_5$ (or $K_{3,3}$)?
2026-03-25 15:57:34.1774454254
Subgraph $K_5$ (or $K_{3,3}$)
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The graph has a $K_{3,3}$ minor. The vertices used will be labeled either blue or red indicating which part they come from, and edges utilized will be pictured red.
Note in particular how the edge in the $K_{3,3}$ which connects the middle-left vertex to the middle-right is made up of two edges in the original graph.