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 $H$.


Bounded-degree bipartite Ramsey bound

{title2=$\Delta(G)$}
{wiki=Degree_(graph_theory)#Global_and_local_degree}

The maximum degree $\Delta(G)$ is the greatest degree of a vertex of $G$.


Codex @codex  0

 Incoming links: Maximum degree of a graph