Timeline for Connected vertex-transitive graph with the fixed-point property
Current License: CC BY-SA 4.0
13 events
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| Apr 19, 2022 at 19:26 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Apr 19, 2022 at 19:25 | comment | added | Dominic van der Zypen | No worries Sam, I wasn't explicit in this question, and thanks for your question dealing explicitly with infinite graphs. | |
| Apr 19, 2022 at 19:24 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Apr 19, 2022 at 19:23 | comment | added | Sam Hopkins | @DominicvanderZypen: Apologies, I did not realize you were also asking about infinite graphs. At any rate, the other question I posted will hopefully resolve this remaining part. | |
| Apr 19, 2022 at 19:22 | comment | added | Dominic van der Zypen | @bof 's comment shows that the question has only been answered for finite graphs -- but your answer, Sam, is so interesting that I decided to accept (and upvote) | |
| Apr 19, 2022 at 19:16 | vote | accept | Dominic van der Zypen | ||
| Apr 19, 2022 at 18:44 | comment | added | Sam Hopkins | @bof I asked this as a new question here: mathoverflow.net/questions/420668/…. | |
| Apr 19, 2022 at 16:14 | comment | added | Sam Hopkins | @AgnishomChattopadhyay: but that is about whether the group is abstractly the automorphism group of a graph, which then tells you nothing about fixed points. | |
| Apr 19, 2022 at 16:12 | comment | added | Agnishom Chattopadhyay | According to mathoverflow.net/questions/37356/… : every (finite or infinite) group is the automorphism group of some graph Taking the fact given by Sam Hopkins and using the above link answers @bof 's question | |
| Apr 19, 2022 at 12:37 | comment | added | Sam Hopkins | @GordonRoyle Of course, the identity is also not a derangement. (And yes it is very easy to find a transitive permutation action on an infinite set with no fixed-point free permutations: e.g. take all permutations which only displace finitely many things.) | |
| Apr 19, 2022 at 10:38 | comment | added | Gordon Royle | There are infinite transitive permutation groups with no derangements other than the identity, but I don’t know if they can be the full automorphism group of a graph. | |
| Apr 19, 2022 at 5:32 | comment | added | bof | Could there be a vertex-transitive infinite graph with no fixed-point-free automorphism? | |
| Apr 18, 2022 at 20:13 | history | answered | Sam Hopkins | CC BY-SA 4.0 |