Decomposability index of tournaments |
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Authors: | Houmem Belkhechine |
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Institution: | Carthage University, Bizerte Preparatory Engineering Institute, Bizerte, Tunisia |
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Abstract: | Given a tournament , a module of is a subset of such that for and , if and only if . The trivial modules of are ,
and . The tournament is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of , denoted by , is the smallest number of arcs of that must be reversed to make indecomposable. For , let be the maximum of over the tournaments with vertices. We prove that and that the lower bound is reached by the transitive tournaments. |
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Keywords: | Tournament Module Indecomposable Inversion Decomposability index |
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