Multipartite lower bound conjecture
Prove or disprove that, for every $m\geq2$ and every $m$-partite graph $H$, one has $#2{^n}{H}\geq #2{^n}{K_m}$ whenever $n$ is sufficiently large in terms of $H$; in particular, determine whether $#2{^n}{H}=\chi(^n)$ for every bipartite graph $H$ in sufficiently large dimension.
References
Is it true that $#2{n}{H}\ge #2{n}{K_m}$ for each $m \ge 2$ and each $m$-partite graph $H$ provided that $n$ is sufficiently large in terms of $H$? In particular, is it true that $#2{n}{H}= \chi(n)$ for each bipartite graph $H$ provided that $n$ is sufficiently large in terms of $H$?
— Ramsey problems for graphs in Euclidean spaces and Cartesian powers
(2512.15516 - Axenovich et al., 17 Dec 2025) in Question Q_partite, Section 6.2 (Growing dimension)