Add to ORKGThe realizability of a graph is the smallest dimension, d, in which for any realization (placement of the vertices) of the graph in any N-dimensional Euclidean space, there exists a realization of the graph with the same edge lengths in d-dimensional Euclidean space. Expanding on the work of Belk and Connelly who determined the set of all forbidden minors for dimensions up to 3, we determine a large family of forbidden minors for each dimension greater than 3. At the heart of this graph family is a new concept, spherical realizability, which places the vertices of a graph on a d-sphere, rather than in Euclidean space. In addition, we prove theorems regarding rigidity and realizability, and we bound above and below the realizability of certa...
International audienceThe number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by de...
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite ...
A bar-joint framework $(G,p)$ in the Euclidean space $\mathbb{E}^d$ is globally rigid if it is the u...
The Gram dimension gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignment of...
We use the ideas of stress theory and tensegrities to answer some questions in discrete geometry. In...
The Gram dimension \rm gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignmen...
In the Graph Realization Problem (GRP), one is given a graph G, a set of non-negative edge-weights, ...
AbstractFor a graph G, let Γ be either the set Γ1 of cycles of G or the set Γ2 of pairs of disjoint ...
AbstractRecently, a new characterization of rigid graphs was introduced using Euclidean distance mat...
For a graph G, let Γ be either the set Γ1 of cycles of G or the set Γ2 of pairs of disjoint cycles o...
A planar graph is said to be trivializable if every regular projection produces a trivial embedding ...
A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each ...
We address a central question in rigidity theory, namely to bound the number of Euclidean or spheric...
AbstractLet G=(V,E,ω) be an incomplete graph with node set V, edge set E, and nonnegative weights ωi...
The Gram dimension gd(G) of a graph G is the smallest inte- ger k ≥ 1 such that any partial real sym...
International audienceThe number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by de...
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite ...
A bar-joint framework $(G,p)$ in the Euclidean space $\mathbb{E}^d$ is globally rigid if it is the u...
The Gram dimension gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignment of...
We use the ideas of stress theory and tensegrities to answer some questions in discrete geometry. In...
The Gram dimension \rm gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignmen...
In the Graph Realization Problem (GRP), one is given a graph G, a set of non-negative edge-weights, ...
AbstractFor a graph G, let Γ be either the set Γ1 of cycles of G or the set Γ2 of pairs of disjoint ...
AbstractRecently, a new characterization of rigid graphs was introduced using Euclidean distance mat...
For a graph G, let Γ be either the set Γ1 of cycles of G or the set Γ2 of pairs of disjoint cycles o...
A planar graph is said to be trivializable if every regular projection produces a trivial embedding ...
A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each ...
We address a central question in rigidity theory, namely to bound the number of Euclidean or spheric...
AbstractLet G=(V,E,ω) be an incomplete graph with node set V, edge set E, and nonnegative weights ωi...
The Gram dimension gd(G) of a graph G is the smallest inte- ger k ≥ 1 such that any partial real sym...
International audienceThe number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by de...
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite ...
A bar-joint framework $(G,p)$ in the Euclidean space $\mathbb{E}^d$ is globally rigid if it is the u...