Infinitesimal rigidity in normed planes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866909075067895808 |
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| author | Dewar, Sean |
| author_facet | Dewar, Sean |
| contents | We prove that a graph has an infinitesimally rigid placement in a non-Euclidean normed plane if and only if it contains a $(2,2)$-tight spanning subgraph. The method uses an inductive construction based on generalised Henneberg moves and the geometric properties of the normed plane. As a key step, rigid placements are constructed for the complete graph $K_4$ by considering smoothness and strict convexity properties of the unit ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_06022 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Infinitesimal rigidity in normed planes Dewar, Sean Metric Geometry 52C25, 52A21 We prove that a graph has an infinitesimally rigid placement in a non-Euclidean normed plane if and only if it contains a $(2,2)$-tight spanning subgraph. The method uses an inductive construction based on generalised Henneberg moves and the geometric properties of the normed plane. As a key step, rigid placements are constructed for the complete graph $K_4$ by considering smoothness and strict convexity properties of the unit ball. |
| title | Infinitesimal rigidity in normed planes |
| topic | Metric Geometry 52C25, 52A21 |
| url | https://arxiv.org/abs/1812.06022 |