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cs.DM2021
A proof of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{ó}w in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we…
cs.DS2021★ 22 cited
Complexity and algorithms for injective edge-coloring in graphs
Florent Foucaud, Hervé Hocquard, Dimitri Lajou
An injective -edge-coloring of a graph is an assignment of colors, i.e. integers in , to the edges of such that any two edges each incident with one d…
math.CO2021
On a List Variant of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with so that no two adjacent vertices are incident to the same sum of labels. In the last decades…