9 citations · 9 across the 4 of their papers we have counts for
6 papers · 1 filter
1-2 Conjectures for Graphs with Low Degeneracy Properties
Julien Bensmail, Beatriz Martins, Chaoliang Tang
In a recent work, Keusch proved the so-called 1-2-3 Conjecture, raised by Karoński, Łuczak, and Thomason in 2004: for every connected graph different from , we can assign labe…
The Maker-Breaker Largest Connected Subgraph Game
Julien Bensmail, Foivos Fioravantes, Fionn Mc Inerney +2
Given a graph and , we introduce the following game played in . Each round, Alice colours an uncoloured vertex of red, and then Bob colours one blue (i…
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…
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…
Decomposing graphs into a constant number of locally irregular subgraphs
Julien Bensmail, Martin Merker, Carsten Thomassen
A graph is locally irregular if no two adjacent vertices have the same degree. The irregular chromatic index of a graph is the smallest number of locally irre…