6 problems

Let $k$ be a positive integer, and call a graph an obstruction for the class of $k$-letter graphs if it is not a $k$-letter graph while all of its proper induced subgraphs are $k$-…

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 unbound…

Let $(G_n)_{n \geq 1}$ be a family of linked chain graphs with linking permutations $\pi_1,\pi_2,\dots$, and let $\mathcal X$ be the hereditary closure of this family. Write…

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…

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 $\lambda$.…

A graph class is minimal of unbounded $\sigma$ if it has unbounded $\sigma$, while every proper hereditary subclass has bounded $\sigma$. Minimal-class conjecture for $\sigma$. Eve…