I'm struggling with finding 3-regular, connected bipartite planar graphs on 14 vertices. I tried starting with a cycle on all vertices but I couldn't quite get a planar graph. Can someone help?
2026-03-29 08:35:48.1774773348
Existence of 3-regular connected bipartite planar graphs of order 14
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It can be done, try $6$ faces bounded by 4-cycles, and $3$ by 6-cycles. It can be shown that an example must be 2-connected, so starting with a cycle was a good idea.
For an example graph, click the spoiler below.