Cranston–Rabern equivalent form of the Borodin–Kostochka conjecture

Let $G$ be a simple graph. Write $\chi=\chi(G)$ for its chromatic number and $\Delta=\Delta(G)$ for its maximum degree. For graphs $G_1$ and $G_2$, let $G_1\lor G_2$ denote their join, and let $E_t$ be the edgeless graph on $t$ vertices. Cranston–Rabern equivalent conjecture. Every graph with $\chi=\Delta=9$ contains $K_3\lor E_6$ as a subgraph. This formulation is stated to be completely equivalent to the Borodin–Kostochka conjecture and focuses the problem on the minimum relevant maximum degree, $9$; it remains open.