Upper tail bounds for irregular graphs

We consider the upper tail large deviations of subgraph counts for irregular graphs $\mathrm{H}$ in $\mathbb{G}(n,p)$, the sparse Erdős-Rényi graph on $n$ vertices with edge connectivity probability $p \in (0,1)$. For $n^{-1/Δ} \ll p \ll 1$, where $Δ$ is the maximum degree of $\mathrm{H}$, we derive