The additive lower bound for m-eternal vertex cover

Let $G=(V,E)$ be a connected graph, let $H$ be a subgraph of $G$, and let $G[V\setminus V(H)]$ be the subgraph induced by the vertices outside $H$. Write $\delta(\cdot)$ for minimum degree and let $\tau_{\mathrm{m}}^{\infty}$ denote the m-eternal vertex cover number. The additive eternal vertex cover conjecture. If

$$\delta(H)\geq2\quad\text{and}\quad\delta(G[V\setminus V(H)])\geq2,$$

then

$$\tau_{\mathrm{m}}^{\infty}(G)\geq\tau_{\mathrm{m}}^{\infty}(H)+\tau_{\mathrm{m}}^{\infty}(G[V\setminus V(H)]).$$

The source presents this as an open conjecture in the eternal vertex-cover model.