8 problems

A CPR graph is a permutation representation graph associated with a string C-group representation. For each $n$, consider the permutation representation graphs of rank $r\geq n/2$…

Let $\mu$ be a periodic nonconstant $0$-$1$ word, and let $G_{\mu}$ be the graph associated with $\mu$. A bound of a hereditary class of finite structures is a structure not in the…

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…

Let $[n]=\{1,2,\dots,n\}$, and consider the graph on the permutations of $[n]$ in which two permutations are adjacent when they are distinguishable in the aforementioned graph-theo…

Permutation-graph 3-edge-colourability conjecture. Every cyclically 5-edge-connected permutation graph is 3-edge-colourable.