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Jul 21 at 2:42 comment added Brendan McKay Regarding maximal planar graphs of minimum degree 5, they can all be made using three operations starting at the icosahedron. See below Fig 7 at users.cecs.anu.edu.au/~bdm/papers/plantri-full.pdf . Now try to prove that if there is an odd hole before an operation, there is one afterwards too. I didn't attempt it.
Jul 20 at 13:21 history edited Licheng Zhang CC BY-SA 4.0
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Jul 20 at 13:05 history asked Licheng Zhang CC BY-SA 4.0