On Certain Spanning Subgraphs of Random Graphs

IF 0.8 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2025-12-09 DOI:10.1134/S1064562425700176

O. I. Serkova

引用次数: 0

Abstract

An improvement of Riordan’s result on the threshold probability of the occurrence of a spanning subgraph in a random graph is obtained for some classes of subgraphs. In particular, this result implies an improved bound for the maximum power of a Hamiltonian cycle in a random graph. Moreover, a sharp asymptotic threshold probability for a random graph to contain spanning subgraphs from a wide class of \(k\)-degenerate graphs is found.

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关于随机图的若干生成子图

对随机图中生成子图的阈值概率给出了Riordan结果的改进。特别地，这个结果暗示了随机图中哈密顿循环的最大功率的改进界。此外，我们还发现了随机图包含大量\(k\) -退化图的生成子图的尖锐渐近阈值概率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications.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.