Vanishing ratio of irredundant and mixed Ramsey numbers

Determine whether, for every fixed integer m greater than or equal to 3, the ratio s(m,n)/t(m,n) tends to zero as n tends to infinity, where s(m,n) is the irredundant Ramsey number and t(m,n) is the mixed Ramsey number.

Background

The irredundant Ramsey number s(m,n) is the least N such that every red-blue coloring of K_N contains either an m-element irredundant set in the blue graph or an n-element irredundant set in the red graph. The mixed Ramsey number t(m,n) uses an n-element independent set in the red graph instead.

Because every independent set is irredundant, the paper records the inequality s(m,n) ≤ t(m,n) ≤ r(m,n). Mynhardt and Roux posed the unresolved question of whether the first ratio s(m,n)/t(m,n) also vanishes asymptotically for every fixed m.