Schelp's minimum-degree Ramsey conjecture for paths

Let $P_n$ denote the path on $n$ vertices, and let $r(P_n,P_n)$ be its two-color Ramsey number. Set

$$t=r(P_n,P_n),$$

where $n$ is sufficiently large. A graph arrows $(P_n,P_n)$ when every 2-edge-coloring of it contains a monochromatic copy of $P_n$. Schelp's conjecture. If $G$ is a graph of order $t$ with minimum degree $\delta(G)>\frac{3}{4}t$, then

$$G\longmapsto(P_n,P_n).$$

The conjecture asks whether the minimum-degree condition forces the same monochromatic path Ramsey property at the order equal to the Ramsey number; its resolution is not given in the source.