A counter-example to Baranyai's combinatorial characterisation for 3-rigidity
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911402471456768 |
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| author | Dewar, Sean |
| author_facet | Dewar, Sean |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19460 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A counter-example to Baranyai's combinatorial characterisation for 3-rigidity Dewar, Sean Combinatorics 52C25 (Primary) 05C50 (Secondary) 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. |
| title | A counter-example to Baranyai's combinatorial characterisation for 3-rigidity |
| topic | Combinatorics 52C25 (Primary) 05C50 (Secondary) |
| url | https://arxiv.org/abs/2601.19460 |