Balanced complete multipartite blow-up
= Balanced complete multipartite blow-up
{title2=$K_r(t)$}
The balanced complete multipartite blow-up $K_r(t)$ replaces each <vertex> of the <complete graph> $K_r$ by an <independent set> of $t$ <vertices>, placing every possible <edge> between different sets and none inside a set. Every fixed <graph> of <chromatic number> at most $r$ embeds into $K_r(t)$ for sufficiently large $t$.