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Claim. The answer is yes. N. Alon, Independent sets in regular graphs and sum-free subsets of finite groups, Israel J. Math. 73 (1991), no. 2, 247--256, proves that the number $f(n)$ of sum-free subsets of $\{1,\ldots,n\}$ is $2^{n/2+o(n)}$, by counting independent sets in regular graphs as the title announces; with the trivial lower bound $f(n)\ge2^{\lceil n/2\rceil}$ (every subset of the integers in $(n/2,n]$ is sum-free) this is the displayed statement $f(n)=2^{(1+o(1))n/2}$ of Problem 748. Calkin proved the same bound independently (Calkin 1990), and Erdős and Granville proved it in unpublished work. It is the exponent form only: the Cameron–Erdős conjecture proper, $f(n)=O(2^{n/2})$, and the two-valued asymptotic $f(n)\sim c_n2^{n/2}$ are the later theorems of Green 2003 and [[problems/integer_sequences/E0748/claims/2003_01_01_sapozhenko|Sapozhenko 2003]].

Reading. The paper is not held in this repository and was not read. Its statement is taken from the introduction of Green's paper, whose display (1) and Proposition 12 credit $|\mathrm{SF}(N)|=2^{N/2+o(N)}$ to Alon, Calkin and Erdős–Granville (the card green_2004_cameron_erdos_conjecture), and from the Crossref record of the DOI, which gives the title as cited here, the venue, volume 73, issue 2, pages 247--256 and the print date of June 1991; the page name carries the first day of that month. Green's bibliography prints the title with "abelian groups" in place of the record's "finite groups".

Acceptance. Refereed: the Israel Journal of Mathematics is a refereed journal, the refereed evidence. The site's curator credits Green and Sapozhenko and not Alon, so no reviewed evidence is listed. Nothing here is this project's own review.

Depends on. No page of this wiki.