Minh's symbolic-power regularity conjecture for edge ideals

Let $G$ be a graph, let $I(G)$ be its edge ideal, and let $I(G)^{(s)}$ denote its $s$-th symbolic power. The invariant ${\rm reg}(-)$ denotes Castelnuovo–Mumford regularity. For every integer $s\geq 1$, Minh's conjecture.

$${\rm reg}(I(G)^s)={\rm reg}(I(G)^{(s)}).$$

The conjecture asks whether ordinary and symbolic powers of every graph edge ideal have the same regularity. It is presented as a conjecture posed by Minh and is related to the study of regularity of symbolic powers; no general resolution is given in the source.