Szczegóły publikacji
Opis bibliograficzny
A general decomposition theory for the 1-2-3 Conjecture and locally irregular decompositions / Olivier Baudon, Julien Bensmail, Tom Davot, Hervé Hocquard, Jakub PRZYBYŁO, Mohammed Senhaji, Éric Sopena, Mariusz WOŹNIAK // Discrete Mathematics and Theoretical Computer Science ; ISSN 1462-7264. — 2019 — vol. 21 iss. 1 art. no. 2, s. 1–14. — Bibliogr. s. 14. — Publikacja dostępna online od: 2019-04-02. — ICGT 2018 : 10th International Colloquium on Graph Theory and Combinatorics : July 9–13, 2018, Lyon, France
Autorzy (8)
- Baudon Olivier
- Bensmail Julien
- Davot Tom
- Hocquard Hervé
- AGHPrzybyło Jakub
- Senhaji Mohammed
- Sopena Éric
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 123894 |
|---|---|
| Data dodania do BaDAP | 2020-01-12 |
| Tekst źródłowy | URL |
| Rok publikacji | 2019 |
| Typ publikacji | referat w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Discrete Mathematics and Theoretical Computer Science |
Abstract
How can one distinguish the adjacent vertices of a graph through an edge-weighting? In the last decades, this question has been attracting increasing attention, which resulted in the active field of distinguishing labellings. One of its most popular problems is the one where neighbours must be distinguishable via their incident sums of weights. An edge-weighting verifying this is said neighbour-sum-distinguishing. The popularity of this notion arises from two reasons. A first one is that designing a neighbour-sum-distinguishing edge-weighting showed up to be equivalent to turning a simple graph into a locally irregular (i.e., without neighbours with the same degree) multigraph by adding parallel edges, which is motivated by the concept of irregularity in graphs. Another source of popularity is probably the influence of the famous 1-2-3 Conjecture, which claims that such weightings with weights in {1, 2, 3} exist for graphs with no isolated edge. The 1-2-3 Conjecture has recently been investigated from a decompositional angle, via so-called locally irregular decompositions, which are edge-partitions into locally irregular subgraphs. Through several recent studies, it was shown that this concept is quite related to the 1-2-3 Conjecture. However, the full connexion between all those concepts was not clear. In this work, we propose an approach that generalizes all concepts above, involving coloured weights and sums. As a consequence, we get another interpretation of several existing results related to the 1-2-3 Conjecture. We also come up with new related conjectures, to which we give some support.