Linear maximum-degree conditions for exact asymmetric Ramsey numbers

Determine whether the exact asymmetric Ramsey-number conclusion of Theorem 1, namely R(T,S)=\underline{R}(T,S) for trees satisfying s_2\geq t_2 and \nu\geq t_1, remains valid when the sublinear maximum-degree assumptions \Delta(T)\leq cn/\log n and \Delta(S)\leq c\nu/\log\nu are replaced by the linear bounds \Delta(T)\leq cn and \Delta(S)\leq c\nu.

Background

The main theorem establishes the exact lower bound R(T,S)=\underline{R}(T,S) for pairs of trees under sublinear maximum-degree conditions, together with the bipartition-size assumptions s_2\geq t_2 and \nu\geq t_1. In contrast, the symmetric result cited as Theorem 1.1 permits linear maximum-degree bounds. The authors explain that the extremal argument used in the symmetric case relies essentially on T=S and does not directly extend to distinct trees.