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.
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Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2018, vol. 20 no. 2
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https://hal.archives-ouvertes.fr/hal-01374427
Contributeur : Julien Bensmail <>
Soumis le : samedi 29 septembre 2018 - 21:33:31
Dernière modification le : lundi 5 novembre 2018 - 15:36:03

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  • HAL Id : hal-01374427, version 5

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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〉

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