Timeline for Aperiodic graphs
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2015 at 23:11 | comment | added | Jamie Walton | Yes, this idea seems pretty natural. It will work in examples such as Cayley graphs of free groups, by simply decorating each infinite path as a Fibonacci tiling. But the issue is when things aren't free, so that one needs to check that the decorations of paths are consistent on overlaps! | |
| Mar 9, 2015 at 23:04 | history | edited | Jamie Walton | CC BY-SA 3.0 |
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| Mar 9, 2015 at 8:30 | comment | added | domotorp | @Daniel: Same here, this was my first idea too. | |
| Mar 8, 2015 at 22:51 | comment | added | Dan Rust | When I first saw this question, my initial idea was to try and decorate all infinite paths with aperiodic sequences (like the fibonacci as mentioned above), but the difficulty seems to be in how to guarantee that one doesn't leave arbitrarily large gaps in the graph. If there was some sufficiently nice class of graphs that all graphs of your type can be identified as subgraphs of, that might make the problem a bit more manageable. | |
| Mar 8, 2015 at 22:36 | comment | added | Jesús Álvarez | So the Fibonacci tiling gives an affirmative answer to the question for $\mathbb Z$, and there are similar constructions solving the problem for $\mathbb Z^d$. I'd like to have an affirmative answer for any graph of bounded geometry without modifying the graph, only equipping it with a decoration having a finite number of values. Could some version of the Fibonacci tiling on the line work for any graph of bounded geometry? | |
| Mar 8, 2015 at 17:25 | history | answered | Jamie Walton | CC BY-SA 3.0 |