Lower Bounds on the Number of Realizations of Rigid Graphs

DOI10.1080/10586458.2018.1437851zbMath1442.05044arXiv1710.08237OpenAlexW3101761638WikidataQ97524448 ScholiaQ97524448MaRDI QIDQ5114449

Christoph Koutschan, Elias P. Tsigaridas, Georg Grasegger

Publication date: 23 June 2020

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.08237

zbMATH Keywords

graph realizationLaman graphminimally rigid graph

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Planar graphs; geometric and topological aspects of graph theory (05C10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Graph algorithms (graph-theoretic aspects) (05C85)

Related Items (3)

New upper bounds for the number of embeddings of minimally rigid graphs ⋮ Coupler curves of moving graphs and counting realizations of rigid graphs ⋮ On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs

Uses Software

• FGb
• LamanGraphs

Cites Work

• Mixed volume techniques for embeddings of Laman graphs
• Computing the number of realizations of a Laman graph
• Equivalent realisations of a rigid graph
• The number of embeddings of minimally rigid graphs
• On spaces of infinitesimal motions and three dimensional Henneberg extensions
• On the number of realizations of certain Henneberg graphs arising in protein conformation
• On graphs and rigidity of plane skeletal structures
• Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs
• Universal Rigidity and Edge Sparsification for Sensor Network Localization
• Molecular distance geometry methods: from continuous to discrete
• Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs
• FGb: A Library for Computing Gröbner Bases
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