厄尔多斯-雷尼随机图中的诱导森林和树

IF 0.5 4区数学 Q3 MATHEMATICS Doklady Mathematics Pub Date : 2024-05-02 DOI:10.1134/S1064562424701886

M. B. Akhmejanova, V. S. Kozhevnikov

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引用次数: 0

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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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.