Bounded-degree bipartite Ramsey bound
= Bounded-degree bipartite Ramsey bound
If a bipartite graph $H$ has $k$ vertices and <maximum degree of a graph>[maximum degree] $d$, then
$$
R(H)=O(d^{2d}k).
$$
A <dependent random choice> argument finds, in one colour, enough vertices whose every subset of at most $d$ vertices has a large common neighbourhood; a greedy embedding then places $H$.