Szczegóły publikacji
Opis bibliograficzny
On locally irregular decompositions and the 1-2 Conjecture in digraphs / Olivier Baudon, Julien Bensmail, Jakub PRZYBYŁO, Mariusz WOŹNIAK // Discrete Mathematics and Theoretical Computer Science ; ISSN 1462-7264. — 2018 — vol. 20 no. 2 art. no. 7, s. 1–11. — Bibliogr. s. 10–11
Autorzy (4)
- Baudon Olivier
- Bensmail Julien
- AGHPrzybyło Jakub
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 117874 |
|---|---|
| Data dodania do BaDAP | 2018-11-10 |
| Tekst źródłowy | URL |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Discrete Mathematics and Theoretical Computer Science |
Abstract
The 1-2 Conjecture raised by Przybylo and Wozniak in 2010 asserts that every undirected graph admits a 2-total-weighting such that the sums of weights "incident" to the vertices yield a proper vertex-colouring. Following several recent works bringing related problems and notions (such as the well-known 1-2-3 Conjecture, and the notion of locally irregular decompositions) to digraphs, we here introduce and study several variants of the 1-2 Conjecture for digraphs. For every such variant, we raise conjectures concerning the number of weights necessary to obtain a desired total-weighting in any digraph. We verify some of these conjectures, while we obtain close results towards the ones that are still open.