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Journal Articles Discussiones Mathematicae Graph Theory Year : 2018

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

Abstract

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.

Dates and versions

hal-04555481 , version 1 (23-04-2024)

Identifiers

Cite

Youssef Boudabbous, Pierre Ille. The {-2,-1}-selfdual and decomposable tournaments. Discussiones Mathematicae Graph Theory, 2018, 38 (3), pp.743. ⟨10.7151/dmgt.2059⟩. ⟨hal-04555481⟩
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