Details

Autor(en) / Beteiligte

• Boudabbous, Youssef
• Ille, Pierre

Titel

The {-2,-1}-selfdual and decomposable tournaments

Ist Teil von

• Discussiones Mathematicae. Graph Theory, 2018, Vol.38 (3)

Ort / Verlag

University of Zielona Góra

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals

Beschreibungen/Notizen

• We only consider finite tournaments. The dual of a tournament is ob- tained by reversing all the arcs. A tournament is selfdual if it is isomorphic to its dual. Given a tournament T, a subset X of V(T) is a module of T if each vertex outside X dominates all the elements of X or is dominated by all the elements of X. A tournament T is decomposable if it admits a module X such that 1 < |X| < |V (T)|.We characterize the decomposable tournaments whose subtournaments obtained by removing one or two vertices are selfdual. We deduce the fol- lowing result. Let T be a non decomposable tournament. If the subtournaments of T obtained by removing two or three vertices are selfdual, then the subtournaments of T obtained by removing a single vertex are not decomposable. Lastly, we provide two applications to tournaments reconstruction.