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

Youssef Boudabbous (1) , Pierre Ille (2)

1 KSU - King Saud University [Riyadh]
2 I2M - Institut de Mathématiques de Marseille

We only consider finite tournaments. The dual of a tournament is obtained 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 < vertical bar X vertical bar < vertical bar V(T)vertical bar. We characterize the decomposable tournaments whose subtournaments obtained by removing one or two vertices are selfdual. We deduce the following 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.

Mots clés: tournament; decomposable; selfdual

Domaines: Combinatoire [math.CO]

Youssef Boudabbous, Pierre Ille. The {-2,-1}-selfdual and decomposable tournaments. Discussiones Mathematicae Graph Theory, 2018, 38 (3), pp.743 - 789. ⟨10.7151/dmgt.2059⟩. ⟨hal-02014259⟩