Burr–Erdős linear Ramsey conjecture for bounded-degree graphs

Let $\Delta\in\mathbb{N}$. A graph has bounded maximum degree at most $\Delta$ when $\Delta(G)\leq\Delta$. Burr–Erdős conjecture. There exists $c=c(\Delta)>0$ such that every $2$-edge-colored $K_n$ contains a monochromatic copy of every graph $G$ with at most $cn$ vertices and $\Delta(G)\leq\Delta$. This is a foundational linear Ramsey-number conjecture for sparse graphs; the supplied source does not indicate whether this formulation is resolved.