Abstract
We prove that the size of the maximum induced forest (of bounded and unbounded degree) in the binomial random graph \(G(n,p)\) for \({{C}_{\varepsilon }}{\text{/}}n < p < 1 - \varepsilon \) with an arbitrary fixed \(\varepsilon > 0\) is concentrated in an interval of size \(o(1{\text{/}}p)\). We also show 2-point concentration for the size of the maximum induced forest (and tree) of bounded degree in \(G(n,p)\) for p = const.
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Funding
Kozhevnikov’s research was supported by the Russian Science Foundation, project no. 21-71-10092. Akhmejanova’s work on Theorem 3 was supported by the Russian Science Foundation (project no. 22-21-00202), and her work on Theorems 1, 2, and 4 was supported by King Abdullah University of Science and Technology (KAUST). Akhmejanova was the winner of the 2020 “Young Mathematician of Russia” award, and she thanks the organizers and the jury for their vote of confidence.
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Translated by I. Ruzanova
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Akhmejanova, M.B., Kozhevnikov, V.S. Induced Forests and Trees in Erdős–Rényi Random Graph. Dokl. Math. (2024). https://doi.org/10.1134/S1064562424701886
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DOI: https://doi.org/10.1134/S1064562424701886