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- W2794035839 abstract "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." @default.
- W2794035839 created "2018-03-29" @default.
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- W2794035839 date "2018-01-01" @default.
- W2794035839 modified "2023-09-27" @default.
- W2794035839 title "The {-2,-1}-selfdual and decomposable tournaments" @default.
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- W2794035839 doi "https://doi.org/10.7151/dmgt.2059" @default.
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