Szczegóły publikacji
Opis bibliograficzny
The role of the Axiom of Choice in proper and distinguishing colourings / Marcin STAWISKI // Ars Mathematica Contemporanea ; ISSN 1855-3966. — 2023 — vol. 23 no. 3, s. 1–8. — Bibliogr. s. 7–8, Abstr. — Publikacja dostępna online od: 2023-02-02
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 146888 |
|---|---|
| Data dodania do BaDAP | 2023-06-12 |
| Tekst źródłowy | URL |
| DOI | 10.26493/1855-3974.2863.4b9 |
| Rok publikacji | 2023 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Ars Mathematica Contemporanea |
Abstract
Call a colouring of a graph distinguishing if the only automorphism which preserves it is the identity. We investigate the role of the Axiom of Choice in the existence of certain proper or distinguishing colourings in both vertex and edge variants with special emphasis on locally finite connected graphs. We show that every locally finite connected graph has a distinguishing colouring with at most countable number of colours or every locally finite connected graph has a proper colouring with at most countable number of colours if and only if Konig's Lemma holds. This statement holds for both vertex and edge colourings. Furthermore, we show that it is not provable in ZF that such colourings exist even for every connected graph with maximum degree 3. We also formulate a few conditions about distinguishing and proper colourings which are equivalent to the Axiom of Choice.
