9 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 $G$ be a regular lattice graph with no global circuits, let $n=v(G)$ tend to infinity, and let ${\cal B}$ denote the resulting set of points in the complex $q$-plane. Conjectur…

Let $G$ be a regular lattice graph with no global circuits, and let $q_0$ be a chromatic zero of $G$. Conjecture (1a). One has $Re(q_0)\geq 0$, and the only chromatic zero with…

Falgas-Ravry–Pfenninger conjecture. There exists some $n\geq 3$ such that

Falgas-Ravry–Pfenninger conjecture. There exists some $n\geq 3$ for which

Let $N\geq 3$, $1\leq p<N$, and let $p^{\ast}$ denote the critical Sobolev exponent. For a function $u$ on $\mathbb{Z}^{N}$, define the discrete $p$-Laplacian by … for $p>1$, with…

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…