Houmem Belkhechine

activity

20102023

most citedIndecomposable tournaments and their indecomposable subtournaments on 5 and 7 vertices

3 citations · 5 across the 6 of their papers we have counts for

collaborators

7 papers

math.CO2023

Irreducible pairings and indecomposable tournaments

Houmem Belkhechine, Cherifa Ben Salha, Rim Romdhane

We only consider finite structures. With every totally ordered set $V$ and a subset $P$ of $(2 V)$ , we associate the underlying tournament $Inv (V, P)$ obta…

math.CO2021

Making a tournament indecomposable by one subtournament-reversal operation

Houmem Belkhechine, Cherifa Ben Salha

Given a tournament $T$ , a module of $T$ is a subset $M$ of $V (T)$ such that for $x, y \in M$ and $v \in V (T) ∖ M$ , $(v, x) \in A (T)$ if and only if $(v, y) \in A (T)$ . The trivial…

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

Primarily orientable graphs

Houmem Belkhechine

A graph $G$ is primarily orientable if it is possible to orient its edges in such a way that the resulting oriented graph is prime, i.e., indecomposable under modular decomposition…

math.CO2020

Decomposability and co-modular indices of tournaments

Houmem Belkhechine, Cherifa Ben Salha

Given a tournament $T$ , a module of $T$ is a subset $X$ of $V (T)$ such that for $x, y \in X$ and $v \in V (T) ∖ X$ , $(x, v) \in A (T)$ if and only if $(y, v) \in A (T)$ . The trivial…

math.CO2013

The indecomposable tournaments $T$ with $∣ W_{5} (T) ∣=∣ T ∣ - 2$

Houmem Belkhechine, Imed Boudabbous, Kaouthar Hzami

We consider a tournament $T = (V, A)$ . For $X \subseteq V$ , the subtournament of $T$ induced by $X$ is $T [X] = (X, A \cap (X \times X))$ . An interval of $T$ is a subset $X$ of $V$ suc…

math.CO2010★ 3 cited

Indecomposable tournaments and their indecomposable subtournaments on 5 and 7 vertices

Houmem BELKHECHINE, Imed BOUDABBOUS

Given a tournament T=(V,A), a subset X of $V$ is an interval of T provided that for every a, b in X and x\in V-X, (a,x) in A if and only if (b,x) in A. For example, $\emptyset$ , {x…