Constructing reflection-symmetric flexible realisations of graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915664257613824 |
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| author | Dewar, Sean Grasegger, Georg Legerský, Jan |
| author_facet | Dewar, Sean Grasegger, Georg Legerský, Jan |
| contents | We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexible realisations. This condition is based on a specific type of edge colouring, where edges are assigned one of three colours in a symmetric way. From some of these colourings we also construct concrete reflection-symmetric realisations with their corresponding symmetry preserving motion. We study also a specific class of reflection-symmetric realisations consisting of triangles and parallelograms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing reflection-symmetric flexible realisations of graphs Dewar, Sean Grasegger, Georg Legerský, Jan Combinatorics 52C25, 70B15, 05C70 We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexible realisations. This condition is based on a specific type of edge colouring, where edges are assigned one of three colours in a symmetric way. From some of these colourings we also construct concrete reflection-symmetric realisations with their corresponding symmetry preserving motion. We study also a specific class of reflection-symmetric realisations consisting of triangles and parallelograms. |
| title | Constructing reflection-symmetric flexible realisations of graphs |
| topic | Combinatorics 52C25, 70B15, 05C70 |
| url | https://arxiv.org/abs/2408.06928 |