Timeline for Is the Rado graph the unique countable graph that has all finite graphs as induced subgraphs?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2023 at 21:29 | vote | accept | Vilhelm Agdur | ||
| Nov 29, 2023 at 14:01 | answer | added | Peter LeFanu Lumsdaine | timeline score: 8 | |
| Nov 29, 2023 at 2:23 | comment | added | tomasz | bof's example generalises to any free amalgamation class. Given one, the disjoint union of all elements of the class is always universal, but it's only very rarely the Fraisse limit. | |
| Nov 28, 2023 at 20:07 | comment | added | bof | It doesn't even have to contain Rado's graph; just take a disjoint union of finite graphs, one of each isomorphism type. | |
| Nov 28, 2023 at 15:05 | comment | added | Emil Jeřábek | @NeilStrickland You don’t need to assume connectedness. This characterization is more-or-less what “Fraïssé limit” means. | |
| Nov 28, 2023 at 14:44 | comment | added | Neil Strickland | I think that if (1) $G$ is connected and countable, and (2) for every finite graph $A$ and full subgraph $B$, any full embedding of $B$ in $G$ extends to a full embedding of $A$, then $G$ is isomorphic to the Rado graph. | |
| Nov 28, 2023 at 14:33 | comment | added | Vilhelm Agdur | Once again my intuition for infinity turns out to be infinitely flawed. (Or at least I have yet to find an upper bound for its flawedness.) Thank you. | |
| Nov 28, 2023 at 13:55 | comment | added | Will Brian | I think there are many examples. The Rado graph plus an isolated point, or plus $n$ isolated points, the disjoint union of two Rado graphs, the disjoint union of all finite graphs . . . | |
| Nov 28, 2023 at 13:50 | history | asked | Vilhelm Agdur | CC BY-SA 4.0 |