Highly regular vertex-transitive graphs are globally rigid
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908770562473984 |
|---|---|
| author | Saliby, Angelo El |
| author_facet | Saliby, Angelo El |
| contents | A graph is said to be globally rigid in $d$-dimensional space if almost all of its embeddings are unique up to isometries. If a graph has enough automorphisms to send any of its vertices into any other, then it is called vertex-transitive. We show that, in any dimension, highly regular vertex-transitive graphs are globally rigid, positively answering a conjecture of Sean Dewar. Furthermore, we construct examples that show that our constant for regularity is best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11240 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Highly regular vertex-transitive graphs are globally rigid Saliby, Angelo El Combinatorics 52C25 A graph is said to be globally rigid in $d$-dimensional space if almost all of its embeddings are unique up to isometries. If a graph has enough automorphisms to send any of its vertices into any other, then it is called vertex-transitive. We show that, in any dimension, highly regular vertex-transitive graphs are globally rigid, positively answering a conjecture of Sean Dewar. Furthermore, we construct examples that show that our constant for regularity is best possible. |
| title | Highly regular vertex-transitive graphs are globally rigid |
| topic | Combinatorics 52C25 |
| url | https://arxiv.org/abs/2601.11240 |