22 citations · 34 across the 13 of their papers we have counts for
21 papers
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…
Generalising the achromatic number to Zaslavsky's colourings of signed graphs
Julien Bensmail, François Dross, Nacim Oijid +1
The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of the graph chromatic th…
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…
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…
On a combination of the 1-2-3 Conjecture and the Antimagic Labelling Conjecture
Julien Bensmail, Mohammed Senhaji, Kasper Szabo Lyngsie
This paper is dedicated to studying the following question: Is it always possible to injectively assign the weights to the edges of any given graph (with no comp…
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…
A Proof of the Barát-Thomassen Conjecture
Julien Bensmail, Ararat Harutyunyan, Tien-Nam Le +2
The Barát-Thomassen conjecture asserts that for every tree on edges, there exists a constant such that every -edge-connected graph with size divisible by can…
On oriented cliques with respect to push operation
Julien Bensmail, Soumen Nandi, Sagnik Sen
To push a vertex of a directed graph is to change the orientations of all the arcs incident with . An oriented graph is a directed graph without any cyc…
List coloring digraphs
Julien Bensmail, Ararat Harutyunyan, Ngoc Khang Le
The dichromatic number of a digraph is the least number such that the vertex set of can be partitioned into parts each of which induces an acyclic subdig…
Disjoint cycles of different lengths in graphs and digraphs
Julien Bensmail, Ararat Harutyunyan, Ngoc Khang Le +2
Understanding how the cycles of a graph or digraph behave in general has always been an important point of graph theory. In this paper, we study the question of finding a set of $k…
Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture
Julien Bensmail, Ararat Harutyunyan, Tien-Nam Le +1
The Barát-Thomassen conjecture asserts that there is a function such that for every fixed tree with edges, every graph which is -edge-connected with its number of…
Orienting edges to fight fire in graphs
Julien Bensmail, Nick Brettell
We investigate a new oriented variant of the Firefighter Problem. In the traditional Firefighter Problem, a fire breaks out at a given vertex of a graph, and at each time interval…
Strong edge-coloring of -bipartite graphs
Julien Bensmail, Aurélie Lagoutte, Petru Valicov
A strong edge-coloring of a graph is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose one part is of max…
Analogous to cliques for (m,n)-colored mixed graphs
Julien Bensmail, Christopher Duffy, Sagnik Sen
Vertex coloring of a graph with -colors can be equivalently thought to be a graph homomorphism (edge preserving vertex mapping) of to the complete graph of order $…
Strong edge-colouring of sparse planar graphs
Julien Bensmail, Ararat Harutyunyan, Hervé Hocquard +1
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree has a strong e…