Consider the follwing graph
In the solution manual it says that this graph is planar. But I can't find an embedding in the plane. So my guess is that it is not planar and the solution is wrong
2026-03-26 06:25:40.1774506340
Is the following graph indeed planar
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There is a planar layout, it seems (original on left, embedding on right):
I found this first on paper, then using a graphics editor (yEd). On paper, I started with the two vertices of highest degree (a & f) as a pair, then added other vertices as necessary. An alternative is to pick a large cycle, then add paths of the remaining edges as bridges to the cycles.