Key points are not available for this paper at this time.
Abstract We investigate the twin‐width of the Erdős‐Rényi random graph . We unveil a surprising behavior of this parameter by showing the existence of a constant such that with high probability, when , the twin‐width is asymptotically , whereas, when or , the twin‐width is significantly higher than . In addition, we show that the twin‐width of is concentrated around within an interval of length . For the sparse random graph, we show that with high probability, the twin‐width of is when .
Ahn et al. (Fri,) studied this question.