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SUBTOURNAMENTS ISOMORPHIC TO W5 OF AN INDECOMPOSABLE TOURNAMENT
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 Title & Authors
SUBTOURNAMENTS ISOMORPHIC TO W5 OF AN INDECOMPOSABLE TOURNAMENT
Belkhechine, Houmem; Boudabbous, Imed; Hzami, Kaouthar;
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 Abstract
We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,) of T induced by X. We say that a tournament T' embeds into a tournament T when T' is isomorphic to a subtournament of T. Otherwise, we say that T omits T'. A subset X of V is a clan of T provided that for a, and , if and only if . For example, , and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class of indecomposable tournaments omitting a certain tournament on 5 vertices. In the case of an indecomposable tournament T, we will study the set (T) of vertices for which there exists a subset X of V such that and T(X) is isomorphic to . We prove the following: for any indecomposable tournament T, if , then -2 and -1 if is even. By giving examples, we also verify that this statement is optimal.
 Keywords
tournament;indecomposable;embedding;critical;
 Language
English
 Cited by
 References
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