Zobrazeno 1 - 10
of 155
pro vyhledávání: '"Cruickshank, James A."'
We show that minimally 3-rigid block-and-hole graphs, with one block or one hole, are characterised as those which are constructible from $K_3$ by vertex splitting, and also, as those having associated looped face graphs which are $(3,0)$-tight. This
Externí odkaz:
http://arxiv.org/abs/2309.06804
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank conditions.
Externí odkaz:
http://arxiv.org/abs/2305.18990
We show that, if $\Gamma$ is a point group of $\mathbb{R}^{k+1}$ of order two for some $k\geq 2$ and $\mathcal S$ is a $k$-pseudomanifold which has a free automorphism of order two, then either $\mathcal S$ has a $\Gamma$-symmetric infinitesimally ri
Externí odkaz:
http://arxiv.org/abs/2304.04693
Autor:
Cruickshank, James, Mohammadi, Fatemeh, Motwani, Harshit J, Nixon, Anthony, Tanigawa, Shin-ichi
We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $\mathbb R^d$. In our setting we allow multiple vertices to be constrained to the same line. Under a mild assumption on t
Externí odkaz:
http://arxiv.org/abs/2208.09308
Publikováno v:
Advances in Mathematics, Volume 458, Part A, 2024, 109953
We prove that if $G$ is the graph of a connected triangulated $(d-1)$-manifold, for $d\geq 3$, then $G$ is generically globally rigid in $\mathbb R^d$ if and only if it is $(d+1)$-connected and, if $d=3$, $G$ is not planar. The special case $d=3$ ver
Externí odkaz:
http://arxiv.org/abs/2204.02503
Publikováno v:
In Advances in Mathematics December 2024 458 Part A
We consider the problem of finding an inductive construction, based on vertex splitting, of triangulated spheres with a fixed number of additional edges (braces). We show that for any positive integer $b$ there is such an inductive construction of tr
Externí odkaz:
http://arxiv.org/abs/2107.03829
Autor:
Cruickshank, James, Schulze, Bernd
We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or a rotatio
Externí odkaz:
http://arxiv.org/abs/2006.10519
We give a short proof of a result of Jordan and Tanigawa that a 4-connected graph which has a spanning planar triangulation as a proper subgraph is generically globally rigid in R^3. Our proof is based on a new sufficient condition for the so called
Externí odkaz:
http://arxiv.org/abs/2002.08680
We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$-tight surface graphs in the case of the sphere, the plane, the twice punctured sphere and the torus. In the case of
Externí odkaz:
http://arxiv.org/abs/1909.06545