The Ramsey equivalence conjecture for uniform trees

Let $r\ge 2$, let $T_1$ and $T_2$ be $r$-uniform trees of order $m$, and let $K_n^{(r)}$ be the complete $r$-uniform hypergraph on $n$ vertices. The Ramsey equivalence conjecture for uniform trees.

$$R(T_1,K_n^{(r)};r)=R(T_2,K_n^{(r)};r).$$

This conjecture asserts that the Ramsey number against a complete $r$-uniform hypergraph depends only on the order of the $r$-uniform tree, not on its structure. It is presented as one of several conjectures arising from the work, with no resolution supplied in the source.