Timeline for Structures for random graphs with structure
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2021 at 21:23 | vote | accept | Hans-Peter Stricker | ||
| Aug 18, 2020 at 17:54 | history | edited | M. Winter | CC BY-SA 4.0 |
added 77 characters in body
|
| Aug 18, 2020 at 16:15 | history | edited | M. Winter | CC BY-SA 4.0 |
added 821 characters in body
|
| Aug 18, 2020 at 15:46 | comment | added | M. Winter | @Hans-PeterStricker Okay, uniqueness is a lie. Imagine that you can build finite graphs of type $(3.3)^3$ by wrapping around the tiling to a torus as you did with $(4)^4$. The Local Theorm assumes that the "topology is simply connected" (e.g. sphere, Euclidean/hyperbolic plane). Similar wrapping might be possible in the spherical and hyperbolic case. I am not sure what this does to vertex-transitivity, but I am optimistic that it is preserved. I might edit the answer later. | |
| Aug 18, 2020 at 15:46 | comment | added | Hans-Peter Stricker | Note that $(3.3)^3 = (3)^6$. Note further that $(6)^3$ gives rise to the hexagonal tiling (which you know for sure). | |
| Aug 18, 2020 at 15:41 | history | edited | M. Winter | CC BY-SA 4.0 |
added 1022 characters in body
|
| Aug 18, 2020 at 15:36 | comment | added | M. Winter | @Hans-PeterStricker The graph with configuration $(3.n)^m$ exists, is unique and vertex-transitive. I edited my answer. | |
| Aug 18, 2020 at 15:35 | history | edited | M. Winter | CC BY-SA 4.0 |
added 1022 characters in body
|
| Aug 18, 2020 at 14:33 | comment | added | Hans-Peter Stricker | And thanks a lot for the counter example! This was my impression, too: that it is tricky to check a configuration for realizability. By the way: I always tended to consider only "tame" configurations of the form $(3.n)^m$ - these should work. Or do some of them don't pass your rule-of-thumb test? | |
| Aug 18, 2020 at 13:49 | history | edited | M. Winter | CC BY-SA 4.0 |
edited body
|
| Aug 18, 2020 at 13:38 | history | edited | M. Winter | CC BY-SA 4.0 |
added 500 characters in body
|
| Aug 18, 2020 at 13:31 | comment | added | Hans-Peter Stricker | Thanks for the hint to the Dolbilin-Schulte paper! | |
| Aug 18, 2020 at 13:30 | history | edited | M. Winter | CC BY-SA 4.0 |
deleted 43 characters in body
|
| Aug 18, 2020 at 13:26 | comment | added | Hans-Peter Stricker | As I do .......;-) | |
| Aug 18, 2020 at 13:25 | comment | added | M. Winter | @Hans-PeterStricker Sadly no, I always do it by hand. | |
| Aug 18, 2020 at 13:25 | history | edited | M. Winter | CC BY-SA 4.0 |
deleted 126 characters in body
|
| Aug 18, 2020 at 13:20 | comment | added | Hans-Peter Stricker | Do you have a tool at hand that draws graphs for given configurations? | |
| Aug 18, 2020 at 13:19 | history | edited | M. Winter | CC BY-SA 4.0 |
deleted 126 characters in body
|
| Aug 18, 2020 at 13:15 | comment | added | Hans-Peter Stricker | Thanks, your answer is relevant in two respects: First, it shows that a graph that realizes a configuration doesn't have to be vertex-transitive. (That's important for me to know, and it answers question 3) Second it shows that there are (of course) configurations that tile only the sphere (defining a polyhedron) but not a plane. This case was excluded in the remark to question 1. | |
| Aug 18, 2020 at 13:12 | history | answered | M. Winter | CC BY-SA 4.0 |