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Journal Articles Combinatorica Year : 2022

A proof of the Multiplicative 1-2-3 Conjecture


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.
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Dates and versions

hal-03324458 , version 1 (23-08-2021)
hal-03324458 , version 2 (16-05-2022)



Julien Bensmail, Hervé Hocquard, Dimitri Lajou, Éric Sopena. A proof of the Multiplicative 1-2-3 Conjecture. Combinatorica, In press. ⟨hal-03324458v2⟩
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