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Journal Articles Discussiones Mathematicae Graph Theory Year : 2018

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


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.
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hal-02014259 , version 1 (11-01-2022)



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⟩
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