A counter-example to Baranyai's combinatorial characterisation for 3-rigidity
Sean Dewar
TL;DR
This paper presents a counter-example to Baranyai's combinatorial characterization of 3-dimensional graph rigidity and offers an alternative proof of the necessary condition, challenging previous assumptions.
Contribution
It provides the first known counter-example to the sufficiency of Baranyai's condition for 3-rigidity and offers an alternative proof of the necessary condition.
Findings
Counter-example disproves sufficiency of Baranyai's condition
Alternative proof confirms the necessity of the condition
Advances understanding of 3-dimensional graph rigidity
Abstract
Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a counter-example to the converse of the condition. Additionally, we provide an alternative proof to the Baranyai's necessary condition.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Computational Geometry and Mesh Generation