4 problems

Consider a graph obtained by a non-trivial stitching of the lattices $\mathbb{Z}^{d}$ and $2\mathbb{Z}^{d}$. Stitching isotropy conjecture. Any such graph is an isotropic graph. If…

Let $\mathbb{L}^d$ denote the $d$-dimensional lattice. Define … Let $d\in\mathbb{N}$ with $d\geq 2$, and let $r\in\mathbb{N}$ with $r\geq r_0(d)$. Component-size conjecture. With h…

4-adjacency cycle conjecture. The image $X$ is non-rigid and irreducible if and only if $X$ is isomorphic to $C_n$ for some $n>4$.

Existence conjecture. Let $H$ be a finite path or a Cartesian product of two finite paths. Then a $t$-PDDS$[H]$ in $\Lambda_n$ exists if and only if at least one of the following h…