Rigidity of nearly planar classes of graphs
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917599397281792 |
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| author | Dewar, Sean Grasegger, Georg Kastis, Eleftherios Nixon, Anthony Servatius, Brigitte |
| author_facet | Dewar, Sean Grasegger, Georg Kastis, Eleftherios Nixon, Anthony Servatius, Brigitte |
| contents | We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic 3-dimensional rigidity matroid adding to the short list of graph classes for which 3-dimensional rigidity is understood. We then analyse global rigidity for these graph classes and use our results to deduce bounds on the maximum likelihood threshold of graphs in these nearly planar classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of nearly planar classes of graphs Dewar, Sean Grasegger, Georg Kastis, Eleftherios Nixon, Anthony Servatius, Brigitte Combinatorics Metric Geometry 52C25 (Primary) O5C10, 62H22 (Secondary) We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic 3-dimensional rigidity matroid adding to the short list of graph classes for which 3-dimensional rigidity is understood. We then analyse global rigidity for these graph classes and use our results to deduce bounds on the maximum likelihood threshold of graphs in these nearly planar classes. |
| title | Rigidity of nearly planar classes of graphs |
| topic | Combinatorics Metric Geometry 52C25 (Primary) O5C10, 62H22 (Secondary) |
| url | https://arxiv.org/abs/2402.17499 |