Szczegóły publikacji
Opis bibliograficzny
On a directed variation of the 1-2-3 and 1-2 conjectures / Emma Barme, Julien Bensmail, Jakub PRZYBYŁO, Mariusz WOŹNIAK // Discrete Applied Mathematics ; ISSN 0166-218X. — 2017 — vol. 217 pt. 2, s. 123–131. — Bibliogr. s. 131, Abstr. — Publikacja dostępna online od: 2016-09-11
Autorzy (4)
- Barme Emma
- Bensmail Julien
- AGHPrzybyło Jakub
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 109359 |
|---|---|
| Data dodania do BaDAP | 2017-10-19 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.dam.2016.08.013 |
| Rok publikacji | 2017 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Applied Mathematics |
Abstract
In this paper, we consider the following question, which stands as a directed analogue of the well-known 1-2-3 Conjecture: Given any digraph D with no arc (uv) over right arrow verifying d(+) (u) = d(-) (v) = 1, is it possible to weight the arcs of D with weights among {1, 2, 3} so that, for every arc (uv) over right arrow of D, the sum of incident weights out-going from u is different from the sum of incident weights in-coming to v? We answer positively to this question, and investigate digraphs for which even the weights among {1, 2} are sufficient. In relation with the so-called 1-2 Conjecture, we also consider a total version of the problem, which we prove to be false. Our investigations turn to have interesting relations with open questions related to the 1-2-3 Conjecture.
