Szczegóły publikacji
Opis bibliograficzny
A note on a directed version of the 1-2-3 Conjecture / Mirko Horňák, Jakub PRZYBYŁO, Mariusz WOŹNIAK // Discrete Applied Mathematics ; ISSN 0166-218X. — 2018 — vol. 236, s. 472–476. — Bibliogr. s. 476, Abstr. — Publikacja dostępna online od: 2017-12-06
Autorzy (3)
- Horňák Mirko
- AGHPrzybyło Jakub
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 117877 |
|---|---|
| Data dodania do BaDAP | 2018-11-10 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.dam.2017.11.016 |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Applied Mathematics |
Abstract
The least k such that a given digraph D = (V, A) can be arc-labeled with integers in the interval [1, k] so that the sum of values in-coming to x is distinct from the sum of values out-going from y for every arc (x, y) epsilon A, is denoted by (chi) over bar (e)((sis))(D). This corresponds to one of possible directed versions of the well-known 1-2-3 Conjecture. Unlike in the case of other possibilities, we show that (chi) over bar (e)((sis))(D) is unbounded in the family of digraphs for which this parameter is well defined. However, if the family is restricted by excluding the digraphs with so-called lonely arcs, we prove that (chi) over bar (e)((sis))(D) <= 4, and we conjecture that (chi) over bar (e)((sis))(D) <= 3 should hold. (C) 2017 Elsevier B.V. All rights reserved.