Abstract
We prove that for any \(\varepsilon > 0\) and \({{n}^{{ - \frac{{e - 2}}{{3e - 2}} + \varepsilon }}} \leqslant p = o(1)\) the maximum size of an induced subtree of the binomial random graph \(G(n,p)\) is concentrated asymptotically almost surely at two consecutive points.
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Buitrago Oropeza, J.C. Maximum Induced Trees in Sparse Random Graphs. Dokl. Math. (2024). https://doi.org/10.1134/S1064562424701989
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DOI: https://doi.org/10.1134/S1064562424701989