3 problems

Let $C_n$ be the cycle graph on $n$ vertices, let $C_n^p$ be its $p$-th power, and let $\Delta_3(C_n^p)$ denote its 3-cut complex. Shellability conjecture. The complex…

Let $C_n$ be the cycle graph on $n$ vertices, let $C_n^2$ be its square, and let $\Delta_k(C_n^2)$ denote its $k$-cut complex. Bayer et al.'s conjecture. Motivated by computational…

Let $G$) be a finite simple graph, let $P_n^2$ be the squared path on $[n]$, and for $k\ge 2$ and $n\ge k+3$ let … where $\Delta_k(P_n^2)$ is the $k$-cut complex of $P_n^2$. Fix…