Tail bounds for Markov equivalence classes of uniform random DAGs

Let $G_n$ be uniform among the simple directed acyclic graphs on $n$ labeled vertices. We prove that its Markov equivalence class satisfies \[ (|(G_n)|>t) C[-c(\frac{ t}{ t})^2] \] for all sufficiently large $t$, uniformly in $n$. This implies the upper tail with exponent $2-\varepsilon$ asked for by Schmid and Sly. The main estimate is a Gaussian tail for the number of vertices incident to reversible edges. Within a large essential-graph component, absence of unshielded colliders is costly; between many small components, their common-parent condition supplies the remaining quadratic cost. Source-layer enumeration transfers these estimates from independent forward edges to the uniform-DAG measure. Complete skeletons show that the logarithmic scale of the bound is sharp up to constants in the exponent.