On a List Variant of the Multiplicative 1-2-3 Conjecture

The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with 1, 2, 3 so that no two adjacent vertices are incident to the same sum of labels. In last decades, several aspects this problem have been studied in literature, including more general versions and slight variations. Notable such variations include List variant, which edges must assigned labels from dedicated lists three labels, Multiplicative different products Several results obtained towards these variants led observe some behaviours distant those original conjecture. work, we consider list version Conjecture, proposing first study very problem. particular, given any graph G, wonder about minimum k G labelled as desired when its size k. Exploiting a relationship between our provide upper bounds on belongs particular classes graphs. We further improve through arguments.