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Twin-width of sparse random graphs

Part of: Graph theory

Published online by Cambridge University Press:  11 December 2024

Kevin Hendrey ,
Sergey Norin ,
Raphael Steiner Open the ORCID record for Raphael Steiner [Opens in a new window]  and
Jérémie Turcotte Open the ORCID record for Jérémie Turcotte [Opens in a new window]
Kevin Hendrey
Affiliation:
Monash University, Melbourne, Australia
Sergey Norin
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, Canada
Raphael Steiner
Affiliation:
Institute of Theoretical Computer Science, Department of Computer Science, ETH Zürich, Switzerland
Jérémie Turcotte*
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, Canada
*
Corresponding author: Jérémie Turcotte; Email: mail@jeremieturcotte.com
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Abstract

We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ for any fixed integer $d \geq 2$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erdős–Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim, and Oum.

Keywords

Twin-widthrandom graphs

MSC classification

Primary: 05C76: Graph operations (line graphs, products, etc.)
Secondary: 05C80: Random graphs

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 34 , Issue 3 , May 2025 , pp. 401 - 420
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

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