Timeline for Maximum automorphism group for a 3-connected cubic graph
Current License: CC BY-SA 3.0
9 events
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| Jul 17, 2013 at 23:38 | history | edited | Brendan McKay | CC BY-SA 3.0 |
fixed typo
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| Jul 17, 2013 at 13:32 | comment | added | verret | In the cubic vertex-transitive case and n twice an odd number, it immediately follows from the same paper that you get a polynomial rather than exponential upper bound. For example Corollary 4 yields that, for large enough n, we have |G|<n^2. This is not best possible, but is not far off, at least for some values of n. If you need more precise estimates, I can show you a few more references that deal with this. (By the way, the link in your "added" section has a typo.) | |
| Jul 17, 2013 at 5:30 | history | edited | Brendan McKay | CC BY-SA 3.0 |
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| Jul 17, 2013 at 5:19 | comment | added | Brendan McKay | @verret: Any idea what the maximum is for transitive cubic graphs of order an odd multiple of 2? | |
| Jul 17, 2013 at 5:18 | history | edited | Brendan McKay | CC BY-SA 3.0 |
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| Jul 17, 2013 at 3:53 | history | edited | Brendan McKay | CC BY-SA 3.0 |
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| Jul 17, 2013 at 3:42 | comment | added | Brendan McKay | Great! I vaguely remembered such a paper but hadn't managed to find it today. | |
| Jul 17, 2013 at 2:54 | comment | added | verret | The family of vertex-transitive graphs you have in mind are in fact best possible among large enough cubic vertex-transitive graphs. (n=100 or so should already suffice.) This is shown in the paper : "Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs", arxiv.org/abs/1010.2546. Therefore, a counter-example to your conjecture will necessarily be not vertex-transitive. | |
| Jul 17, 2013 at 1:29 | history | asked | Brendan McKay | CC BY-SA 3.0 |