A proof of the Multiplicative 1-2-3 Conjecture
Discrete Mathematics
2022-05-19 v2 Combinatorics
Abstract
We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{\'o}w 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.
Cite
@article{arxiv.2108.10554,
title = {A proof of the Multiplicative 1-2-3 Conjecture},
author = {Julien Bensmail and Hervé Hocquard and Dimitri Lajou and Éric Sopena},
journal= {arXiv preprint arXiv:2108.10554},
year = {2022}
}