Skip to Main content Skip to Navigation
Journal articles

On locally irregular decompositions and the 1-2 Conjecture in digraphs

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download
Contributor : Julien Bensmail <>
Submitted on : Saturday, September 29, 2018 - 9:33:31 PM
Last modification on : Tuesday, December 8, 2020 - 9:42:18 AM
Long-term archiving on: : Monday, December 31, 2018 - 10:51:06 AM


Files produced by the author(s)


  • HAL Id : hal-01374427, version 5


Olivier Baudon, Julien Bensmail, Jakub Przybyło, Mariusz Woźniak. On locally irregular decompositions and the 1-2 Conjecture in digraphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2018, vol. 20 no. 2. ⟨hal-01374427v5⟩



Record views


Files downloads