Borel distinguishing number
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911157075312640 |
|---|---|
| author | Bilge, Onur Kaya, Burak |
| author_facet | Bilge, Onur Kaya, Burak |
| contents | In this paper, we study definable variants of the notion of the distinguishing number of a graph in descriptive set theoretic setting. We introduce the notion of the Borel distinguishing number of a Borel graph and provide examples that separate distinguishing number and Borel distinguishing number at various levels. More specifically, we prove that there exist Borel graphs with countable distinguishing number but uncountable Borel distinguishing number and that, for every integer $n \geq 3$, there exists a Borel graph with distinguishing number $2$ whose Borel distinguishing number is finite and at least $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borel distinguishing number Bilge, Onur Kaya, Burak Logic 03E15, 05C25 In this paper, we study definable variants of the notion of the distinguishing number of a graph in descriptive set theoretic setting. We introduce the notion of the Borel distinguishing number of a Borel graph and provide examples that separate distinguishing number and Borel distinguishing number at various levels. More specifically, we prove that there exist Borel graphs with countable distinguishing number but uncountable Borel distinguishing number and that, for every integer $n \geq 3$, there exists a Borel graph with distinguishing number $2$ whose Borel distinguishing number is finite and at least $n$. |
| title | Borel distinguishing number |
| topic | Logic 03E15, 05C25 |
| url | https://arxiv.org/abs/2508.08201 |