A Proof of the Molecular Conjecture

We prove the Molecular Conjecture posed by Tay and Whiteley. This implies that a graph G can be realized as an infinitesimally rigid panel-hinge framework in ℝ d by mapping each vertex to a rigid panel and each edge to a hinge if and only if contains edge-disjoint spanning trees, where is the graph...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 45; no. 4; pp. 647 - 700
Main Authors Katoh, Naoki, Tanigawa, Shin-ichi
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.06.2011
Springer Nature B.V
Subjects
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Geometry
Graphs
Hinges
Mapping
Mathematics
Mathematics and Statistics
Molecular chemistry
Panels
Proving
Panel-hinge frameworks
Molecular frameworks
Combinatorial rigidity
Rigid realizations
The molecular conjecture
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Summary:We prove the Molecular Conjecture posed by Tay and Whiteley. This implies that a graph G can be realized as an infinitesimally rigid panel-hinge framework in ℝ d by mapping each vertex to a rigid panel and each edge to a hinge if and only if contains edge-disjoint spanning trees, where is the graph obtained from G by replacing each edge by parallel edges.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-011-9348-6