P. Ille

activity

20112021

most citedDetermination of the prime bound of a graph

3 citations · 9 across the 6 of their papers we have counts for

collaborators

6 papers

math.CO2021★ 2 cited

Partially critical 2-structures

Houmem Belkhechine, Imed Boudabbous, Pierre Ille

A 2-structure $σ$ consists of a vertex set $V (σ)$ and of an equivalence relation $\equiv_{σ}$ defined on $(V (σ) \times V (σ)) ∖ {(v, v) : v \in V (σ)}$ . Given a 2-structure $σ$ , a s…

math.CO2020

Critical 3-hypergraphs (detailed version)

Abderrahim Boussairi, Brahim Chergui, Pierre Ille +1

Given a 3-hypergraph $H$ , a subset $M$ of $V (H)$ is a module of $H$ if for each $e \in E (H)$ such that $e \cap M \neq = \emptyset$ and $e ∖ M \neq = \emptyset$ , there exists $m \in M$ …

math.CO2018★ 2 cited

3-uniform hypergraphs: modular decomposition and realization by tournaments

Abderrahim Boussaïri, Brahim Chergui, Pierre Ille +1

Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V (T) = V (H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V (T)$ that induce 3-cyc…

math.CO2014

Primitive bound of a 2-structure

Abderrahim Boussaïri, Pierre Ille, Robert E. Woodrow

A 2-structure on a set $S$ is given by an equivalence relation on the set of ordered pairs of distinct elements of $S$ . A subset $C$ of $S$ , any two elements of which appear the sa…

math.CO2013★ 3 cited

Determination of the prime bound of a graph

Abderrahim Boussaïri, Pierre Ille

Given a graph $G$ , a subset $M$ of $V (G)$ is a module of $G$ if for each $v \in V (G) ∖ M$ , $v$ is adjacent to all the elements of $M$ or to none of them. For instance, $V (G)$ …

math.CO2011★ 2 cited

Prime bound of a graph

Abderrahim Boussaïri, Pierre Ille

Given a graph G, a subset M of V (G) is a module of G if for each v \in V (G) \diagdownM, v is adjacent to all the elements of M or to none of them. For instance, V(G), \varnothing…