  We study the single-site Glauber dynamics for the fugacity $\lambda$,
Hard-core model on the random graph $G(n, d/n)$. We show that for the typical
instances of the random graph $G(n,d/n)$ and for fugacity $\lambda <
\frac{d^d}{(d-1)^{d+1}}$, the mixing time of Glauber dynamics is $n^{1 +
O(1/\log \log n)}$.
  Our result improves on the recent elegant algorithm in [Bezakova, Galanis,
Goldberg Stefankovic; ICALP'22]. The algorithm there is a MCMC based sampling
algorithm, but it is not the Glauber dynamics. Our algorithm here is simpler,
as we use the classic Glauber dynamics. Furthermore, the bounds on mixing time
we prove are smaller than those in Bezakova et al. paper, hence our algorithm
is also faster.
  The main challenge in our proof is handling vertices with unbounded degrees.
We provide stronger results with regard the spectral independence via branching
values and show that the our Gibbs distributions satisfy the approximate
tensorisation of the entropy. We conjecture that the bounds we have here are
optimal for $G(n,d/n)$.
  As corollary of our analysis for the Hard-core model, we also get bounds on
the mixing time of the Glauber dynamics for the Monomer-dimer model on
$G(n,d/n)$. The bounds we get for this model are slightly better than those we
have for the Hard-core model
