Diameter and long paths in critical digraph
We study the random directed graph $\vec G(n,p)$ in which each of the $n(n-1)$ possible directed edges are present with probability $p$. We show that in the critical window the longest self avoiding oriented paths in $\vec G(n,p)$ have length $O_{\mathbb{P}}(n^{1/3})$ so $\vec G(n,p)$ has diameter $...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
08.05.2023
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Subjects | |
Online Access | Get full text |
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Summary: | We study the random directed graph $\vec G(n,p)$ in which each of the
$n(n-1)$ possible directed edges are present with probability $p$. We show that
in the critical window the longest self avoiding oriented paths in $\vec
G(n,p)$ have length $O_{\mathbb{P}}(n^{1/3})$ so $\vec G(n,p)$ has diameter
$O_{\mathbb{P}}(n^{1/3})$. |
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DOI: | 10.48550/arxiv.2305.04815 |