On the maximal number of real embeddings of minimally rigid graphs in \(\mathbb{R}^2,\mathbb{R}^3\) and \(S^2\)

DOI10.1016/j.jsc.2019.10.015zbMath1448.05144arXiv1811.12800OpenAlexW2902145203MaRDI QIDQ2200306

Ioannis Z. Emiris, Evangelos Bartzos, Jan Legerský, Elias P. Tsigaridas

Publication date: 19 September 2020

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12800

zbMATH Keywords

mixed volumerigid graphLaman graphcoupler curveCayley-Menger matrixreal bound

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Graph representations (geometric and intersection representations, etc.) (05C62) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (6)

The m-Bézout bound and distance geometry ⋮ New upper bounds for the number of embeddings of minimally rigid graphs ⋮ Coupler curves of moving graphs and counting realizations of rigid graphs ⋮ Computing Circuit Polynomials in the Algebraic Rigidity Matroid ⋮ On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs ⋮ An asymptotic upper bound for graph embeddings

Uses Software

• PHCpack
• Matplotlib
• Scikit
• phcpy
• LamanGraphs

Cites Work

• Mixed volume techniques for embeddings of Laman graphs
• The number of roots of a system of equations
• Equivalent realisations of a rigid graph
• The number of embeddings of minimally rigid graphs
• On the number of realizations of certain Henneberg graphs arising in protein conformation
• Generic global rigidity
• 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
• Characterizing generic global rigidity
• The Number of Realizations of a Laman Graph
• A Polyhedral Method for Sparse Systems with Many Positive Solutions
• On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs
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