3 problems

For $m\geq4$, let $\operatorname{ER}(m,4,r)$ denote the off-diagonal unordered Erdős–Rado number in the setting where monochromatic cliques have order $m$, lexical cliques have ord…

Let $\operatorname{ER}(4,4,r)$ denote the off-diagonal unordered Erdős–Rado number when monochromatic and lexical copies of $K_4$ are forbidden and a rainbow clique has order $r$.…

For integers $m,\ell\geq 4$, let $\operatorname{ER}(m,\ell,r)$ denote the off-diagonal unordered Erdős–Rado number for monochromatic and lexical cliques of the indicated orders aga…