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arXiv · 2601.19460

A counter-example to Baranyai's combinatorial characterisation for 3-rigidity

Sean Dewar
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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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Sean Dewar. 2026-01-27. A counter-example to Baranyai's combinatorial characterisation for 3-rigidity. https://arxiv.org/abs/2601.19460

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