4 problems

Sazdanovic–Scofield conjecture. The homological span satisfies

Helme-Guizon–Przytycki–Rong torsion conjecture. The cohomology ${{H_{*,*}}^{\mathcal{A}_m}(G)}$ contains a torsion part if and only if $G$ has no loops and contains a cycle of orde…

Let $G$ be a simple, connected graph with $v$ vertices and girth $\ell$, where $\ell=2k$ or $\ell=2k-1$ according to its parity. Let $P_\ell$ denote the cycle graph of length…

Let $G$ be a graph with $v$ vertices and $b$ blocks, and let $\mathcal{A}_m=\mathbb{Z}[x]/(x^m=0)$. Write $H_{\mathcal{A}_m}(G)$ for its chromatic homology and…