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Apr 18, 2022 at 13:18 comment added wandering_lambda Yes, thus an easy lower bound would be $\sum_{i=1}^3{n \choose i}$.
Apr 18, 2022 at 6:27 comment added Fedor Petrov for the family of all subsets, all sets with at most three elements must be of different color, right?
Apr 17, 2022 at 20:00 history edited wandering_lambda CC BY-SA 4.0
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Apr 17, 2022 at 19:58 comment added wandering_lambda Yes, or any lower bound on it.
Apr 17, 2022 at 19:56 comment added bof In other words, you want the chromatic number of the generalized Kneser graph $K(n,k,2)$.
Apr 17, 2022 at 19:44 history asked wandering_lambda CC BY-SA 4.0