Sharp constant in the Erdős–Rényi Lovász-number asymptotic

Determine the correct constant in the asymptotic formula [?] for the expected Lovász number of the Erdős–Rényi random graph in the regime [?].

Background

The paper reviews prior results for the Lovász number of Erdős–Rényi random graphs. In the dense-to-moderately sparse regime, the expected Lovász number is known only up to order, namely [?]. The authors note that the leading constant in this asymptotic remains unresolved.

References

To the best of our knowledge, determining the correct constant in the \Theta(\sqrt{n/p}) asymptotic remains an open question.

— The Lovász number of random circulant graphs  (2502.16227 - Bandeira et al., 22 Feb 2025) in Section 1, Introduction