Timeline for Given a polytope $P$ with bipartite edge-graph, if the bipartition classes are equal in size and lie on spheres, is $P$ inscribed?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 13, 2022 at 1:08 | vote | accept | M. Winter | ||
| Jun 9, 2022 at 11:44 | comment | added | Ilya Bogdanov | I don’t think it is a large generalization, but you can find even a vertex strictly outside the ball, unless all white vertices are on the same sphere. The argument works literally. Also, surely, bipartiteness can be weakened to the same condition as in Steinitz’s. | |
| Jun 9, 2022 at 11:40 | comment | added | M. Winter | @IlyaBogdanov Thank you very much Ilya! This sounds like a very nice argument. I will need to read it carefully and I will accept the answer once I reached a good understanding :) Can you give me a taste of the most general interesting statement that this argument applies to? I ask because you said "it can be generalized even further". | |
| Jun 9, 2022 at 10:04 | comment | added | Ilya Bogdanov | @SamHopkins Right! Otherwise there will be no green-green edge. (The version of Steinitz’s criterion is still vacuously true...) | |
| Jun 9, 2022 at 10:00 | comment | added | Sam Hopkins | There’s still an implicit $n>2$ assumption here, right? | |
| Jun 9, 2022 at 8:36 | history | answered | Ilya Bogdanov | CC BY-SA 4.0 |