Timeline for Is there a "simplest" way to embed a graph in 3-space?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 21 at 12:12 | comment | added | M. Winter | I just realized the following: $K_7$ has genus 1, so embeds in a torus. It is also intrinsically knotted, so one of its Hamiltonian cycles is knotted. Remove an edge from $K_7$ that is not in this Hamiltonian cycle. The graph still has genus 1, so the previous embedding is "best possible" in terms of genus. But it is not knotless. This is just a comment to show that lowest genus embeddings do not necessarily yield linkless/knotless in all cases where it is possible. | |
| Aug 20 at 12:04 | comment | added | M. Winter | I accepted this answer because it works for all graphs and because it is a nice idea for capturing the topological simplicity (as opposed to geometric simplicity) that I had in mind. | |
| Aug 20 at 9:19 | vote | accept | M. Winter | ||
| Aug 17 at 18:51 | comment | added | M. Winter | This is a very nice idea! | |
| Aug 17 at 1:06 | history | answered | quarague | CC BY-SA 4.0 |