Year: 2025
Type: preprint
Abstract: We study the probabilistic zero forcing process, a probabilistic variant of the classical zero forcing process. We show that for every connected graph $G$ on $n$ vertices, there exists an initial set consisting of a single vertex such that the expected propagation time is $n/2 + O(1)$. This result is tight and confirms a conjecture posed by Narayanan and Sun. Additionally, we show tight bounds on the probabilistic throttling number, which captures the trade-off between the size of the initial set and the speed of propagation. Namely, we show that for every connected graph $G$ on $n$ vertices, there exists an initial set consisting of $O(\sqrt{n})$ vertices such that the expected propagation time is $O(\sqrt{n})$. This improves upon previous results by Geneson and Hogben, and confirms another conjecture by Narayanan and Sun.
Source: arXiv (Cornell University)
Authors: Jelassi, Mehdi, Portier, Julien, Sarkar, Rik
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416960192
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