Global rigidity of periodic graphs under fixed-lattice representations

DOI10.1016/j.jctb.2020.09.009zbMath1457.05097arXiv1612.01379OpenAlexW3088014958MaRDI QIDQ2221925

Bernd Schulze, Viktória E. Kaszanitzky, Shin-ichi Tanigawa

Publication date: 3 February 2021

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.01379

zbMATH Keywords

group-labeled graphglobal rigiditymatroid connectivityperiodic frameworkcylindrical frameworktoroidal framework

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Kinematics of a rigid body (70B10) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Related Items

Flexible placements of periodic graphs in the plane ⋮ Sufficient conditions for the global rigidity of periodic graphs ⋮ Sufficient connectivity conditions for rigidity of symmetric frameworks

Cites Work

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• Gain-sparsity and symmetry-forced rigidity in the plane
• Unique low rank completability of partially filled matrices
• Necessary conditions for the generic global rigidity of frameworks on surfaces
• Necessary conditions for the global rigidity of direction-length frameworks
• Stress matrices and global rigidity of frameworks on surfaces
• Frameworks with forced symmetry. I: Reflections and rotations
• Rigidity and energy
• A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid.
• Connected rigidity matroids and unique realizations of graphs
• Independence and port oracles for matroids, with an application to computational learning theory
• Generic combinatorial rigidity of periodic frameworks
• Global rigidity of generic frameworks on the cylinder
• Sufficient conditions for the global rigidity of graphs
• Inductive constructions for frameworks on a two-dimensional fixed torus
• Frameworks with forced symmetry. II: Orientation-preserving crystallographic groups
• Generic global rigidity
• Globally linked pairs of vertices in equivalent realizations of graphs
• On graphs and rigidity of plane skeletal structures
• Periodic frameworks and flexibility
• Characterizing generic global rigidity
• Conditions for Unique Graph Realizations
• The Rigidity of Graphs
• The rigidity of periodic frameworks as graphs on a fixed torus