Exactness of the general lower bound for more tree pairs

Decide for more families of pairs of trees (T,S) whether the general lower bound R(T,S)\geq\underline{R}(T,S) is tight, that is, whether R(T,S)=\underline{R}(T,S).

Background

The paper proves equality with the general lower bound for a large family of pairs satisfying maximum-degree and bipartition-size conditions, and gives a bounded-degree result when the order of T is sufficiently larger than that of S. The concluding question asks for further families beyond those treated by these results for which the lower bound is exact.