In red/blue/purple colourings of K_n with no red/purple K_s and no blue/purple K_t, the largest possible number of purple edges is asymptotically RT_s(n,t) when t is linear in n with small slope, and is within a constant (or factor 1/2) of RT_3(n,t) when t is sublinear.
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Ramsey with purple edges
In red/blue/purple colourings of K_n with no red/purple K_s and no blue/purple K_t, the largest possible number of purple edges is asymptotically RT_s(n,t) when t is linear in n with small slope, and is within a constant (or factor 1/2) of RT_3(n,t) when t is sublinear.