Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation

A proof of the Multiplicative 1-2-3 Conjecture

Julien Bensmail 1 Hervé Hocquard 2 Dimitri Lajou 2 Éric Sopena 2 
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kaziów in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we can assign labels 1,2,3 to the edges in such a way that no two adjacent vertices are incident to the same product of labels.
Document type :
Complete list of metadata
Contributor : Julien Bensmail Connect in order to contact the contributor
Submitted on : Monday, May 16, 2022 - 10:02:11 PM
Last modification on : Tuesday, June 14, 2022 - 8:26:56 AM


proof123p (1).pdf
Files produced by the author(s)


  • HAL Id : hal-03324458, version 2
  • ARXIV : 2108.10554



Julien Bensmail, Hervé Hocquard, Dimitri Lajou, Éric Sopena. A proof of the Multiplicative 1-2-3 Conjecture. [Research Report] Université côte d'azur; Université de bordeaux. 2021. ⟨hal-03324458v2⟩



Record views


Files downloads