The threshold for the asymmetric vertex-Ramsey property in randomly perturbed graphs

Asier Calbet, Victor Falgas-Ravry, Joseph Hyde

For $r\ge 2$ and graphs $H_1,\dots ,H_r,G$, we say that $G$ is $(H_1,\dots ,H_r)$ vertex-Ramsey, or $(H_1,\dots ,H_r{)}_v$-Ramsey, if whenever we colour the vertices of $G$…