22 citations · 33 across the 7 of their papers we have counts for
9 papers
Algorithms and complexity for geodetic sets on interval and chordal graphs
Dibyayan Chakraborty, Sandip Das, Florent Foucaud +2
We study the computational complexity of finding the geodetic number of a graph on chordal graphs and interval graphs. A set of vertices of a graph is a \textit{geodetic se…
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…
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…
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…
Between proper and strong edge-colorings of subcubic graphs
Hervé Hocquard, Dimitri Lajou, Borut Lu{ž}ar
In a proper edge-coloring the edges of every color form a matching. A matching is induced if the end-vertices of its edges induce a matching. A strong edge-coloring is an edge-colo…
On Cartesian products of signed graphs
Dimitri Lajou
In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromat…
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…
Graph modification for edge-coloured and signed graph homomorphism problems: parameterized and classical complexity
Florent Foucaud, Hervé Hocquard, Dimitri Lajou +2
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph …
On the achromatic number of signed graphs
Dimitri Lajou
In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different…