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Jun 26, 2019 at 2:31 comment added Gordon Royle Well, it is known that we can move from any unlabelled planar triangulation to any other via a sequence of "edge flips" which are operations where an edge $xy$ is removed, thereby creating a 4-face, say $\mathit{xayb}$, and then the edge $ab$ is inserted, restoring the property of being a planar triangulation. After 30 seconds thought, it seems to me that triangulations will be the hardest to deal with, so I'll put my money on yes.
Jun 25, 2019 at 23:44 vote accept Aidan Rocke
Jun 25, 2019 at 18:49 comment added Gerhard Paseman The original title mentioned planar graphs. Any thoughts on a Hpath through the relevant subset (k edges on N labeled vertices)? I suspect the answer is no. Gerhard "Has To Do With Triangles" Paseman, 2019.06.25.
Jun 25, 2019 at 14:17 history undeleted Gordon Royle
Jun 25, 2019 at 14:17 history edited Gordon Royle CC BY-SA 4.0
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Jun 25, 2019 at 11:22 history answered Gordon Royle CC BY-SA 4.0