Burr–Erdős conjecture for degenerate graphs

Let $d\in\mathbb{N}$. A graph is $d$-degenerate when its vertices admit an ordering in which every vertex has at most $d$ neighbors earlier in the ordering. Burr–Erdős conjecture. There exists $c=c(d)>0$ such that every $2$-edge-colored $K_n$ contains a copy of every $d$-degenerate graph on at most $cn$ vertices. The source states that this conjecture was recently confirmed by Lee, so the result is solved.