Chains-in-a-cycle conjecture for bounded lettericity

Let $\mathcal X$ be a graph class with bounded $\lambda$ and unbounded lettericity, and let $\mathcal C_k$ denote the chains-in-a-cycle classes defined earlier in the paper. Chains-in-a-cycle conjecture. If $\mathcal X$ is a class of bounded $\lambda$ and unbounded lettericity, then $\mathcal X$ contains $\mathcal C_k$ for some $k$, or one of the complements of these classes. The preceding theorem handles a restricted cyclic setting, while the conjecture asserts that these constructions and their complements are the only obstacles in the bounded-$\lambda$ setting.