厄尔多斯-雷尼随机图中的诱导森林和树

Pub Date : 2024-05-02 DOI:10.1134/S1064562424701886

M. B. Akhmejanova, V. S. Kozhevnikov

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摘要

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 \）集中在一个大小为 \(o(1{\text{/}}p)\) 的区间内。我们还证明了在 p = const 的情况下，\(G(n,p)\)中最大诱导林（和树）的有界度大小的 2 点集中。

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Induced Forests and Trees in Erdős–Rényi Random Graph

We prove that the size of the maximum induced forest (of bounded and unbounded degree) in the binomial random graph \(G(n,p)\) for \({{C}_{\varepsilon }}{\text{/}}n 0\) 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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