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arXiv · 2312.03688

Twin-width of sparse random graphs

Kevin Hendrey·Sergey Norin·Raphael Steiner·Jérémie Turcotte
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Abstract

We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ 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.

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Kevin Hendrey, Sergey Norin, Raphael Steiner, Jérémie Turcotte. 2023-12-06. Twin-width of sparse random graphs. https://doi.org/10.1017/s0963548324000439

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