5 problems

Let $G_n$ be the Schrijver graph, and let $G_n^{\boxtimes 2}$ denote its strong square. The Schrijver number of a graph $G$, denoted by $\vartheta'(G)$, is the corresponding streng…

Let $k$ and $r$ be integers with $2\leq r\leq k-2$, and let $D(G)$ denote the diameter of a graph $G$. For $n=2k+r$, write $\operatorname{SG}(n,k)$ for the Schrijver graph. Unit-ga…

Let $k$ and $r$ be integers with $r\geq 1$, and let $D(G)$ denote the diameter of a graph $G$. For $n=2k+r$, write $\operatorname{SG}(n,k)$ for the Schrijver graph. Monotonicity co…

Let $d$ be any integer, let $k_d$ be a threshold depending on $d$, and let ${\rm SG}(2k+d,k)$ be the Schrijver graph. An edge is interlacing according to the standard interlacing-e…

For integers $k\geq 1$ and $n\geq 2k+1$, let $QG(n,k)$ be the spanning subgraph of the Schrijver graph $SG(n,k)$ constructed in Theorem 1.1, which is a quadrangulation of…