Timeline for Applications of infinite graph theory
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2022 at 12:45 | answer | added | Agelos | timeline score: 3 | |
| Jun 9, 2017 at 18:03 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Jun 9, 2017 at 16:43 | answer | added | user21574 | timeline score: 7 | |
| Jun 9, 2017 at 16:19 | history | edited | YCor |
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| Jun 9, 2017 at 15:37 | comment | added | Moritz | @Richard Dupont: Check out Diestel, R., Graph Theory, Springer, 4th Edition, 2012. An online version is available with a chapter only about infinite graphs. | |
| Jun 9, 2017 at 15:29 | answer | added | Peter Heinig | timeline score: 3 | |
| Sep 23, 2010 at 9:26 | answer | added | Stefan Geschke | timeline score: 8 | |
| Sep 22, 2010 at 22:26 | answer | added | Tony Huynh | timeline score: 17 | |
| Sep 22, 2010 at 22:23 | comment | added | Terry Tao | In the converse direction, one can view infinite graphs as a discretisation of continuous spaces (and infinite Cayley graphs as a discretisation of homogeneous spaces). Gromov's original proof of his theorem relies on this perspective (or more precisely, the idea that homogeneous spaces can arise as limits of infinite Cayley graphs). So the discrete infinitary theory of infinite graphs form a nice bridge between the discrete finitary world and the continuous infinitary world. | |
| Sep 22, 2010 at 22:12 | answer | added | Colin Reid | timeline score: 12 | |
| Sep 22, 2010 at 21:28 | answer | added | HJRW | timeline score: 13 | |
| Sep 22, 2010 at 21:26 | comment | added | HJRW | Owen - the topological proof is easier, if you already have the machinery of covering spaces to hand. (Which many of us do, but there are others who don't want to think that way.) | |
| Sep 22, 2010 at 21:11 | comment | added | Qiaochu Yuan | I also understand that particular infinite graphs (Bruhat-Tits trees) are important in number theory, but I'm sure an expert could give the scoop on that. I also think you're undervaluing the importance of Cayley graphs (e.g. they were used in the original proof of Gromov's theorem on polynomial growth), but again, an expert should chime in here. | |
| Sep 22, 2010 at 21:06 | answer | added | John Stillwell | timeline score: 28 | |
| Sep 22, 2010 at 20:02 | comment | added | Owen Sizemore | There is a simple proof that every subgroup of a free group is free using infinite graphs and covering spaces. While a purely algebraic proof is not so easy. More generally many interesting facts about groups can be proven based on the fact that they act nicely on infinite graphs. | |
| Sep 22, 2010 at 20:00 | comment | added | Gjergji Zaimi | Random walks or harmonic functions aren't as interesting for finite graphs. | |
| Sep 22, 2010 at 19:48 | comment | added | Qiaochu Yuan | The universal cover of a d-regular finite graph is the d-regular infinite tree. If you care about d-regular finite graphs (e.g. expanders) then you should care about the d-regular infinite tree, right? | |
| Sep 22, 2010 at 19:45 | comment | added | Eric Tressler | To study percolation you basically need an infinite graph to avoid finite-size effects. | |
| Sep 22, 2010 at 19:39 | history | asked | Richard Dupont | CC BY-SA 2.5 |