5 problems

For $n>4$, let $W_n$ be the wheel graph, let $W_n^{out}$ be obtained by deleting an edge from its polygonal part, and let $W_n^{in}$ be obtained by deleting a spike edge. Wheel and…

Let $W_n$ be the wheel graph, the cone over an $(n-1)$-gon, and let $w^1_{{\mathcal A}_3}(W_n)$ denote the width of the torsion in $H^{1,*}_{{\mathcal A}_3}(W_n)$. Width conjecture…

Wheel saturation recurrence. For every integer $k\geq 4$, there exists a constant $N_k$ such that, for all $n>N_k$,

Let $W_{2r+1}$ be the graph formed from a cycle of length $2r+1$ by adding one vertex adjacent to every cycle vertex. For positive integers $r$ and $k$, let $h(n,k,W_{2r+1})$ be th…

Let $W_n$ be the wheel graph on $n$ vertices, and write $V(W_n)$ and $E(W_n)$ for its vertex and edge sets. Let $\operatorname{MH}_{k,k}(W_n)$ denote its magnitude homology on the…