Twin-width of sparse random graphs

We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erd\H{o}s-Renyi and regular random graphs, complementing the bounds in the d...

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Bibliographic Details
Main Authors Hendrey, Kevin, Norin, Sergey, Steiner, Raphael, Turcotte, Jérémie
Format Journal Article
LanguageEnglish
Published 06.12.2023
Subjects
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Summary:We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erd\H{o}s-Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim and Oum.
DOI:10.48550/arxiv.2312.03688