Seven-color packing coloring conjecture for claw-free subcubic graphs

Let $G$ be a claw-free subcubic graph. Seven-color packing coloring conjecture. The graph $G$ is $(2,2,2,2,2,2,2)$-packing colorable. The paper gives related packing-coloring results for claw-free subcubic graphs, but does not establish this seven-color assertion; it remains open.