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Claim. Theorem 1 of S. Gaspers and S. Mackenzie, On the number of minimal separators in graphs, J. Graph Theory 87 (2018), no. 4, 653--659, published online 13 September 2017 (arXiv:1503.01203, first posted 4 March 2015, the claim's date; cited from its v2 of 2 April 2015, p. 3): "$\mathsf{sep}(n)=O(\rho^n\cdot n)$, where $\rho=\frac{1+\sqrt5}2=1.6180\ldots$ is the golden ratio." Here $\mathsf{sep}(n)$ is the largest number of minimal separators, sets that are minimal $(u,v)$-separators for some pair of vertices, of a graph on $n$ vertices; the authors present it as the bound of Fomin and Villanger "with simpler arguments". 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 $c(n)\le\mathsf{sep}(n)$ and the theorem gives $\limsup_n c(n)^{1/n}\le\rho$. The site's commentary on Problem 150 credits the paper with the simpler proof of the upper bound. Read depth: the statement and its one-paragraph proof in the preprint; the journal text was not compared.

The paper's Theorem 2 is a lower bound, $\mathsf{sep}(n)\in \omega(1.4521^n)$ in the arXiv v2 and $\omega(1.4457^n)$ in the abstract of the published version, the figure the site and Bradač print. The published proof is unchecked, so the lower bound is not part of this claim.

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

Depends on. Gaspers--Mackenzie, Theorem 1, the source's result page.

Acceptance. Refereed: the paper is a publication in the Journal of Graph Theory. 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.