Timeline for Graph of number pairs summing to a square number
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2021 at 12:42 | comment | added | Dominic van der Zypen | @VladMatei I knew about the triangle-free graphs. I suspect the chromatic number is $\aleph_0$ -- but my only reason is that infinite graphs tend to have either a trivially provable finite chromatic number - or infinite chromatic number. (Exception: the graph defined on $\mathbb{R}^2$ where points are joined by an edge iff their Euclidean distance is $1$. The chromatic number is known to lie in the interval $[4,7]$.) | |
| Feb 16, 2021 at 14:24 | comment | added | Vlad Matei | Clique number is only a lower bound. On the other there are triangle free graphs with arbitrarily large chromatic number. So my guess that asking about the chromatic number is way harder than asking about the clique number of this graph. | |
| Feb 15, 2021 at 7:29 | comment | added | Dominic van der Zypen | @VladMatei Thanks for your hint, didn't know that! So there are cliques of size 6; is it known whether the chromatic number is strictly larger than 6 - even infinite possibly? | |
| Feb 14, 2021 at 0:01 | comment | added | Gerry Myerson | See also math.stackexchange.com/questions/4022415/… | |
| Feb 13, 2021 at 19:44 | comment | added | Vlad Matei | This last question also showed up on MathOverflow mathoverflow.net/questions/374394/… | |
| Feb 13, 2021 at 19:16 | comment | added | Seva | I suppose, this should be known for the (positive) differences? | |
| Feb 13, 2021 at 16:45 | comment | added | Vlad Matei | Also Bombieri Lang would suggest that the clique number is finite. | |
| Feb 13, 2021 at 16:43 | comment | added | Max Alekseyev | See also math.stackexchange.com/q/1576986 | |
| Feb 13, 2021 at 16:38 | comment | added | Vlad Matei | The clique number is an open problem of Erdos and Moser. Choudhry constructed infinitely many sextuples here worldscientific.com/doi/abs/10.1142/S1793042115500281 | |
| Feb 13, 2021 at 15:44 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |