38 citations · 61 across the 21 of their papers we have counts for
13 papers · 1 filter
Hypergraphs with Polynomial Representation: Introducing -splits
François Pitois, Mohammed Haddad, Hamida Seba +1
Inspired by the split decomposition of graphs and rank-width, we introduce the notion of -splits. We focus on the family of -splits of a graph of order , and we prove that…
Leader Election And Local Identifiers For 3D Programmable Matter
Nicolas Gastineau, Wahabou Abdou, Nader Mbarek +1
In this paper, we present two deterministic leader election algorithms for programmable matter on the face-centered cubic grid. The face-centered cubic grid is a 3-dimensional 12-r…
Coloring of the dth power of the face-centered cubic grid
Nicolas Gastineau, Olivier Togni
The face-centered cubic grid is a three dimensional 12-regular infinite grid. This graph represents an optimal way to pack spheres in the three-dimensional space. In this grid, the…
On S-packing edge-colorings of cubic graphs
Nicolas Gastineau, Olivier Togni
Given a non-decreasing sequence S = (s 1,s 2,. .. ,s k) of positive integers, an S-packing edge-coloring of a graph G is a partition of the edge set of G into k subsets {X 1 ,X 2,.…
On packing chromatic number of subcubic outerplanar graphs
Nicolas Gastineau, P{ř}emysl Holub, Olivier Togni
Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exists subclasses in which the packing chromatic number i…
Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees
Benoit Darties, Nicolas Gastineau, Olivier Togni
The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently compl…
Subdivision into i-packings and S-packing chromatic number of some lattices
Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni
An -packing in a graph is a set of vertices at pairwise distance greater than . For a nondecreasing sequence of integers , the -packing chrom…
A characterization of b-chromatic and partial Grundy numbers by induced subgraphs
Brice Effantin, Nicolas Gastineau, Olivier Togni
Gy{á}rf{á}s et al. and Zaker have proven that the Grundy number of a graph satisfies if and only if contains an induced subgraph called a -atom.The family of…
Completely Independent Spanning Trees in Some Regular Graphs
Benoit Darties, Nicolas Gastineau, Olivier Togni
Let be an integer and be spanning trees of a graph . If for any pair of vertices of , the paths from to in each , $1\le i\l…
S-Packing Colorings of Cubic Graphs
Nicolas Gastineau, Olivier Togni
Given a non-decreasing sequence of positive integers, an {\em -packing coloring} of a graph is a mapping from to $\{s\_1,s\_2, \ldot…
On the family of -regular graphs with Grundy number
Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni
The Grundy number of a graph , denoted by , is the largest such that there exists a partition of , into independent sets and every vertex o…
On Packing Colorings of Distance Graphs
Olivier Togni
The {\em packing chromatic number} of a graph is the least integer for which there exists a mapping from to such that any two vertic…
Extended core and choosability of a graph
Yves Aubry, Godin Jean-Christophe, Togni Olivier
A graph is -choosable if for any color list of size associated with each vertices, one can choose a subset of colors such that adjacent vertices are colored with…