8 papers
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…
On the signed chromatic number of some classes of graphs
Julien Bensmail, Sandip Das, Soumen Nandi +3
A signed graph is a graph along with a function . A closed walk of a signed graph is positive (resp., negative) if it has an even (resp., odd) num…
Further Evidence Towards the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kazi{ó}w in 2012, states that, a few obvious exceptions apart, all graphs can be 3-edge-labelled so that no two…
Pushable chromatic number of graphs with degree constraints
Julien Bensmail, Sandip Das, Soumen Nandi +4
Pushable homomorphisms and the pushable chromatic number of oriented graphs were introduced by Klostermeyer and MacGillivray in 2004. They notably observed that, for any orie…
Extending Drawings of Graphs to Arrangements of Pseudolines
Alan Arroyo, Julien Bensmail, R. Bruce Richter
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two…
Decomposability of graphs into subgraphs fulfilling the 1-2-3 Conjecture
Julien Bensmail, Jakub Przybyło
The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with , and so that adjacent vertices receive distinct weight…