Email this article First-order zero-one law for the uniform model of the random graph
- Authors: Zhukovskii M.E.1,2, Sveshnikov N.M.3
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Affiliations:
- Advanced Combinatorics and Networking Lab, Moscow Institute of Physics and Technology (National Research University)
- Moscow Center for Fundamental and Applied Mathematics
- Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology (National Research University)
- Issue: Vol 211, No 7 (2020)
- Pages: 60-71
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133335
- DOI: https://doi.org/10.4213/sm9321
- ID: 133335
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Abstract
The paper considers the Erdős-Renyi random graph in the uniform model $G(n,m)$, where $m=m(n)$ is a sequence of nonnegative integers such that $m(n)\sim cn^{\alpha}<(2-\varepsilon)n^2$ for some $c>0$, $\alpha\in[0,2]$, and $\varepsilon>0$. It is shown that $G(n,m)$ obeys the zero-one law for the first-order language if and only if either $\alpha\in\{0,2\}$, or $\alpha$ is irrational, or $\alpha\in(0,1)$ and $\alpha$ is not a number of the form $1-1/\ell$, $\ell\in\mathbb{N}$. Bibliography: 15 titles.
About the authors
Maksim Evgen'evich Zhukovskii
Advanced Combinatorics and Networking Lab, Moscow Institute of Physics and Technology (National Research University); Moscow Center for Fundamental and Applied Mathematics
Email: zhukmax@gmail.com
Doctor of physico-mathematical sciences
Nikita Maksimovich Sveshnikov
Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology (National Research University)
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