5 problems

Let $\mathbb{P}_4$ be the prefix-reversal graph on the permutations of $\{1,2,3,4\}$, and let $\gamma(\mathbb{P}_4)$ denote its orientable genus. A graph is a pretzel graph if it a…

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 $M$ be a partial multiplication matrix, meaning a matrix whose nonzero entries are monotone classes, and suppose its cell graph is cyclic. Let $\mathcal X$ be a permutation cla…

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…