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Graph embeddings in the plane, space and sphere - source code and results

Bartzos, Evangelos; Legerský, Jan


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    "description": "<p>This is supplementary material for the paper&nbsp;<em>On the Maximal Number of Real Embeddings of&nbsp;Minimally Rigid Graphs in&nbsp;<span class=\"math-tex\">\\(\\mathbb{R}^2\\)</span>,&nbsp;<span class=\"math-tex\">\\(\\mathbb{R}^3\\)</span>&nbsp;and&nbsp;<span class=\"math-tex\">\\(S^2\\)</span></em>. It includes source code and results. See also&nbsp;the&nbsp;<a href=\"http://jan.legersky.cz/project/spatialgraphembeddings/\">project website</a>. The material extends the results of our <a href=\"https://doi.org/10.1145/3208976.3208994\">conference paper</a> (ISSAC 2018).</p>\n\n<p><strong>Construction of Laman and Geiringer graphs</strong></p>\n\n<p>MATLAB and SageMath code for construction of Laman and&nbsp;Geiringer graphs using Henneberg steps.</p>\n\n<p><strong>Computation of mixed volume and complex solutions</strong></p>\n\n<p>Functions that&nbsp;compute the mixed volume and the (complex) embeddings in the plane, space or sphere of a given graph using different algebraic formulations.</p>\n\n<p><strong>Coupler curve visualization and sampling method</strong></p>\n\n<p>Implementation of&nbsp;our&nbsp;method for obtaining edge lengths of a Geiringer&nbsp;graph with many real spatial embeddings.<br>\nVisualization of coupler curves of the 7-vertex Geiringer graph with the maximal number of&nbsp;real embeddings (G48).</p>\n\n<p><strong>Maple parametric search</strong></p>\n\n<p>Maple worksheet illustrating a method to improve the number of real embeddings of G48 using RootFinding[Parametric] subpackage.</p>\n\n<p><strong>Results</strong></p>\n\n<p>Mixed volumes and numbers of real and complex embeddings in the plane, space and sphere.<br>\nEdge lengths giving high&nbsp;numbers of real embeddings, in the plane, space and sphere.&nbsp;<br>\nMaple script verifying the results.</p>", 
    "language": "eng", 
    "title": "Graph embeddings in the plane, space and sphere - source code and results", 
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        "affiliation": "Department of Informatics and Telecommunications, National Kapodistrian University of Athens, and ATHENA Research Center", 
        "name": "Bartzos, Evangelos"
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        "affiliation": "Research Institute for Symbolic Computation, Johannes Kepler University Linz, Austria", 
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