A proof of the Multiplicative 1-2-3 Conjecture

2021/08/24 by Julien Bensmail, Hervé Hocquard, Bensmail, Julien +5 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · doi:10.48550/arxiv.2108.10554

openalex publication_date 2021/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Every graph is uniform-span (2,2)-choosable: Beyond the 1-2 conjecture

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