Timeline for Can all unit-distance graphs have their vertices at algebraic integers?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2015 at 9:09 | comment | added | Ilya Bogdanov | Thanks! The link to the first one was in my answer, but I did not know about the second. | |
| Jan 28, 2015 at 5:43 | comment | added | David Eppstein | The full version is in Tyszka, Apoloniusz (2000), "Discrete versions of the Beckman-Quarles theorem", Aequationes Mathematicae 59 (1-2): 124–133, doi:10.1007/PL00000119, MR 1741475 | |
| Jan 28, 2015 at 5:43 | comment | added | David Eppstein | A slightly weaker version is that for any algebraic number there is a rigid framework and a configuration of that framework such that the number is a distance between two points in the framework. It's from Maehara, Hiroshi (1991), "Distances in a rigid unit-distance graph in the plane", Discrete Applied Mathematics 31 (2): 193–200, doi:10.1016/0166-218X(91)90070-D | |
| Jan 27, 2015 at 18:25 | comment | added | Ilya Bogdanov | @David: Do you know the exact reference? | |
| Jan 27, 2015 at 8:12 | comment | added | David Eppstein | More generally it is known that one can force any algebraic number to be the distance between some two vertices. | |
| Jan 27, 2015 at 0:13 | vote | accept | Adam P. Goucher | ||
| Jan 26, 2015 at 19:54 | history | edited | Ilya Bogdanov | CC BY-SA 3.0 |
Remark has been expanded
|
| Jan 26, 2015 at 18:54 | history | answered | Ilya Bogdanov | CC BY-SA 3.0 |