7 problems

Stress-linked pair component conjecture. If $\{u,v\}$ is $d$-stress-linked in $G$, then there is some $\mathcal{R}_d$-component $G_0$ of $G$ such that $\{u,v\}$ is $d$-stress-linke…

Stress-linked pair equivalence conjecture. Being $d$-stress-linked is equivalent to being globally $d$-linked.

Full stress-rank conjecture. If $(G,p)$ is globally $(d,k)$-rigid and $G$ is not complete, then there exists $\sigma \in \ker DR_k(G,p)^T$ such that

Let $G$ be a graph and let $u,v\in V(G)$. Let an $\mathcal{R}_d$-component of $G$ be a maximal subgraph determined by the $d$-dimensional rigidity matroid. Stress-linked pair compo…

Let $G$ be a graph and let $u,v\in V(G)$ be a pair of vertices. Let $K(G,p)$ denote the shared stress kernel associated with a generic realization $(G,p)$. Suppose that $\{u,v\}$ i…

Let $G$ be a graph. A pair of vertices $\{u,v\}$ is $d$-stress-linked if it satisfies the stress-based linkage condition introduced in the paper. Rigidity-linked pair conjecture. A…

Alfakih's conjecture. A maximal-rank positive semidefinite equilibrium stress matrix must exist for $(p,\Gamma)$.