TY  - Type of reference 
TI  - [FORTHCOMING] Les tournois indécomposables à indice de Slater minimal 
AU  - Houmem Belkhechine
 
AU  - Cherifa Ben Salha
 
AU  - Rim Romdhane 
AB  - The Slater index (resp. decomposability index) of a tournament is the minimum number of arcs that must be reversed in that tournament in order to make it a total order (resp. indecomposable (under modular decomposition)). The first author [H. Belkhechine, Decomposability index of tournaments, Discrete Math. 340 (2017) 2986–2994] showed that for every integer $$$n \geq 5$$$, the decomposability index of the $$$n$$$-vertex total order equals $$$\left\lceil \frac{n+1}{4} \right\rceil$$$. It follows that the Slater index of an indecomposable $$$n$$$-vertex tournament is at least $$$\left\lceil \frac{n+1}{4} \right\rceil$$$. This led A. Boussaïri to ask the following question during the thesis defense of the second author on July 2, 2021 : what are the indecomposable tournaments $$$T$$$ whose Slater index is minimum over all indecomposable tournaments with the same vertex set as $$$T$$$ ? These tournaments are then the indecomposable tournaments $$$T$$$ obtained from a total order by reversing exactly $$$\left\lceil \frac{v(T)+1}{4} \right\rceil$$$ arcs, where $$$v(T)$$$ is the number of vertices of $$$T$$$. In this paper, we characterize such tournaments by means of so-called irreducible pairings. 
DO  - À venir 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  - Module, pairing, indecomposable, irreducible, decomposability index, Slater index, Module, pairing, indecomposable, irreducible, decomposability index, Slater index,  
L1  -  
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2025/08/11 
SN  - 1869-6090 
TT  - [FORTHCOMING] Indecomposable tournaments with minimum Slater index 
UR  - https://www.openscience.fr/Les-tournois-indecomposables-a-indice-de-Slater-minimal 
IS  - Articles à paraître<br> 
VL  -  
ER  -