PreprintCC BY 4.0arXiv
Probability threshold for the stability of $α(G(n,r,s))$
Abstract
Let G(n,r,s) be a graph (V,E) such that V = binom[n]r and $E = \{(u, v)| |u \cap v| = s\}. $In this paper we study the probability threshold for the exact stability of the independence number of $G(n, r, s)$ where r > 2s+2. We improve the previous result of Pyaderkin that implied asymptotic stability of the independence number.
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BibTeX
@misc{koshelev2026probability,
title = {{Probability threshold for the stability of $α(G(n,r,s))$}},
author = {M. M. Koshelev and A. M. Raigorodskii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00144},
eprint = {2610.00144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probability threshold for the stability of $α(G(n,r,s))$
AU - M. M. Koshelev
AU - A. M. Raigorodskii
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00144
UR - https://arxiv.org/abs/2610.00144
AB - Let G(n,r,s) be a graph (V,E) such that V = binom[n]r and $E = \{(u, v)| |u \cap v| = s\}. $In this paper we study the probability threshold for the exact stability of the independence number of $G(n, r, s)$ where r > 2s+2. We improve the previous result of Pyaderkin that implied asymptotic stability of the independence number.
ER -