Transitive convex subsets in large tournaments

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Abstract

A convex subset of vertices of a tournament T is such that any vertex not in the subset either dominates or is dominated by all of the vertices in the convex subset. Given a large tournament T, we explore the structure of T by looking for its transitive convex subsets. In a majority voting tournament some isolated inconsistencies may appear in such subsets. We propose a way to reveal such “nearly” transitive convex subsets. They are the subsets of a partition which optimizes the inertia of a geometrical embedding of T.

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Cited by (1)

  • The morphology of infinite tournaments; application to the growth of their profile

    2010, European Journal of Combinatorics
    Citation Excerpt :

    Find a result, similar to Theorem 2, for indecomposable tournaments and, possibly, a finitary version. The notion of an acyclically indecomposable tournament was studied by Culus and Jouve in [7,8,14]. The notion of a profile was introduced in 1971 by the second author (see [11,12]) and developed in [18–20]; for a survey see [24].

I am grateful to Alain Guénoche for placing his C programs at my disposal.

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