Timeline for Polytope with indegree-increasing property.
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2015 at 11:52 | answer | added | Hao Chen | timeline score: 3 | |
| Mar 8, 2015 at 23:08 | comment | added | Joseph O'Rourke | @TheMaskedAvenger: Much hinges on the phrase "simple polytope," as HaoChen points out. | |
| Mar 8, 2015 at 19:47 | comment | added | The Masked Avenger | Of course, Joseph O'Rourke makes the same point in a more picturesque way, but the cylinder model might be more amenable to a proof of impossibility. | |
| Mar 8, 2015 at 19:44 | comment | added | The Masked Avenger | Let us decorate cylinders with square and triangular grids, so that there are points with (undirected) degrees of four and six respectively. We can chain these cylinders together to form a graph which, as we travel from one end of the cylinder to the other, gives us alternating sets of degree 4 and degree 6 vertices. I imagine a combinatorial polytope with such alternations as to foil any hope for an index increasing function, regardless of how the cylinder (or stack of prisms) is deformed. | |
| Mar 8, 2015 at 16:54 | comment | added | Hao Chen | I guess that you know Kalai's algorithm for recognising graphs of simple polytopes. | |
| Mar 8, 2015 at 15:44 | answer | added | Joseph O'Rourke | timeline score: 1 | |
| Mar 8, 2015 at 7:53 | history | asked | Yunhyung Cho | CC BY-SA 3.0 |