Minimality of twisted cycles in a chain for unbounded lettericity

Let $\mathcal T$ denote the graph class of twisted cycles in a chain, namely the class represented by the constructions discussed around Figure~. A graph class is minimal of unbounded lettericity if it has unbounded lettericity and every proper hereditary subclass has bounded lettericity. Twisted-cycle minimality conjecture. The class $\mathcal T$ is minimal of unbounded lettericity. This is presented as a slightly weaker conjecture toward the problem of characterizing hereditary graph classes of bounded lettericity; the paper does not resolve it.