A 1-2-3-4 result for the 1-2-3 Conjecture in 5-regular graphs

Julien Bensmail 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : The 1-2-3 Conjecture, posed by Karoński, Łuczak and Thomason, asks whether every connected graph G different from K2 can be 3-edge-weighted so that every two adjacent vertices of G get distinct sums of incident weights. Towards that conjecture, the best-known result to date is due to Kalkowski, Karoński and Pfender, who proved that it holds when relaxed to 5-edge-weightings. Their proof builds upon a weighting algorithm designed by Kalkowski for a total version of the problem. In this work, we present new mechanisms for using Kalkowski's algorithm in the context of the 1-2-3 Conjecture. As a main result we prove that every 5-regular graph admits a 4-edge-weighting that permits to distinguish its adjacent vertices via their incident sums.
Type de document :
Article dans une revue
Discrete Applied Mathematics, Elsevier, In press
Liste complète des métadonnées

Contributeur : Julien Bensmail <>
Soumis le : lundi 1 octobre 2018 - 08:51:22
Dernière modification le : lundi 5 novembre 2018 - 15:36:03


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-01509365, version 2



Julien Bensmail. A 1-2-3-4 result for the 1-2-3 Conjecture in 5-regular graphs. Discrete Applied Mathematics, Elsevier, In press. 〈hal-01509365v2〉



Consultations de la notice


Téléchargements de fichiers