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Claim. Theorem 1 of F. V. Fomin and Y. Villanger, Treewidth computation and extremal combinatorics, Combinatorica 32 (2012), no. 3, 289--308 (arXiv:0803.1321, first posted 9 March 2008, the claim's date; cited from its v2 of 5 May 2008, p. 6): "Let $\Delta_G$ be the set of all minimal separators in a graph $G$ on $n$ vertices. Then $|\Delta_G|=\mathcal O(1.6181^n)$." The base in the proof (p. 7) is the golden ratio $\frac{1+\sqrt5}2$. A minimal separator is a set that is a minimal $(u,v)$-separator for some pair of vertices $u,v$. Every minimal cut $T$ of a graph, a minimal set of vertices whose removal disconnects it, is a minimal $(u,v)$-separator for any $u,v$ in different components of the graph without $T$, so $c(n)\le\mathsf{sep}(n)$, where $\mathsf{sep}(n)$ is the largest number of minimal separators of a graph on $n$ vertices, and the theorem gives $\limsup_n c(n)^{1/n}\le \frac{1+\sqrt5}2$. The site's commentary on Problem 150 credits the paper with the upper end of the best known interval for $\alpha$. Read depth: the statement and its proof (pp. 6--7 of the preprint), with the Main Lemma taken as a statement; the journal text was not compared.

Covers. The bound half of the question: $\limsup_n c(n)^{1/n}\le \frac{1+\sqrt5}2<2$, so the limit, whose existence Bradač proves, is below $2$; the existence of the limit is not addressed.

Depends on. Fomin--Villanger, Theorem 1, the source's result page.

Acceptance. Refereed: the paper is a publication in Combinatorica. The site's curator credits the paper in the problem's commentary, but the site lists no parts and its label credits Bradač's note for the whole problem, so the credit is not listed as reviewed evidence.