Claims

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1984_01_01_hanson_seyffarth: Cayley graphs of cyclic groups on symmetric complete sum-free sets give triangle-free graphs of diameter two whose degree is of order root n along an infinite sequence of n, so f(n) over root n does not tend to infinity.

1994_01_01_furedi_seress: Theorem 6.1 of Füredi and Seress gives, for every large n, a triangle-free graph of diameter two on n vertices with maximum degree at most two over root three times root n plus a lower-order term, so f(n) has order root n.

2017_03_12_haviv_levy: Theorem 1.5 of Haviv and Levy gives a symmetric complete sum-free subset of every large cyclic group of size O(root n), whose Cayley graph is a triangle-free graph of diameter two of degree O(root n); f(n) has order root n.

2026_09_15_korsky: A proof claim posted on the site's proof-claim tab asserts that f(n) is (1+o(1)) root n, the sharp constant Alon conjectured, by a fibered polarity graph; unreviewed, with the proof in an external file.

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