Minimal unbounded-bb classes in hereditary graph classes

A graph class is minimal of unbounded $\lambda$ if it has unbounded $\lambda$, while every proper hereditary subclass has bounded $\lambda$. Minimal-class conjecture for $\lambda$. Every graph class of unbounded $\lambda$ contains a minimal class of unbounded $\lambda$. The paper presents this as an analogue of the established statement for $\gamma$ and does not resolve it.