In this note we confirm a conjecture raised by Benjamini et al. (SIAM J Discrete Math 28(2):767–785, 2014) on the acquaintance time of graphs, proving that for all graphs G with n vertices it holds that AC(G)=O(n3/2)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}(G) = O(n^{3/2})$$\end{document}. This is done by proving that for all graphs G with n vertices and maximum degree Δ\documentclass[12pt]{minimal}
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\begin{document}$$\varDelta $$\end{document} it holds that AC(G)≤20Δn\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}(G) \le 20 \varDelta n$$\end{document}. Combining this with the bound AC(G)≤O(n2/Δ)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}(G) \le O(n^2/\varDelta )$$\end{document} from Benjamini et al. (SIAM J Discrete Math 28(2):767–785, 2014) gives the uniform upper bound of O(n3/2)\documentclass[12pt]{minimal}
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\begin{document}$$O(n^{3/2})$$\end{document} for all n-vertex graphs. This bound is tight up to a multiplicative constant. We also prove that for the n-vertex path Pn\documentclass[12pt]{minimal}
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\begin{document}$$P_n$$\end{document} it holds that AC(Pn)=n-2\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}(P_n)=n-2$$\end{document}. In addition we show that the barbell graph Bn\documentclass[12pt]{minimal}
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\begin{document}$$B_n$$\end{document} consisting of two cliques of sizes ⌈n/2⌉\documentclass[12pt]{minimal}
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\begin{document}$${\lceil n/2\rceil }$$\end{document} and ⌊n/2⌋\documentclass[12pt]{minimal}
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\begin{document}$${\lfloor n/2\rfloor }$$\end{document} connected by a single edge also has AC(Bn)=n-2\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}(B_n) = n-2$$\end{document}. This shows that it is possible to add Ω(n2\documentclass[12pt]{minimal}
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\begin{document}$$\varOmega (n^2$$\end{document}) edges a graph without changing its AC\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {AC}$$\end{document} value.
