| Autor: |
Olivier Baudon, Julien Bensmail, Jakub Przybyło, Mariusz Woźniak |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol vol. 20 no. 2, Iss Graph Theory (2018) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.23638/DMTCS-20-2-7 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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