A 16-vertex tournament for which Banks set and Slater set are disjoint

Irène Charon; Olivier Hudry; Frédéric Woirgard

doi:10.1016/s0166-218x(97)88689-1

A 16-vertex tournament for which Banks set and Slater set are disjoint

Irène Charon
, Olivier Hudry
, Frédéric Woirgard

Ecole Nationale Supérieure des Télécoms

Research output: Contribution to journal › Article › peer-review

Abstract

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Slater winner of T is the first vertex of any transitive tournament at minimum distance of T (the distance being the number of arcs to reverse in T to make T transitive). In this note, we show that there exists a tournament with 16 vertices for which no Slater winner is a Banks winner. This counterexample improves the previous one, due to G. Laffond and J.-F. Laslier, which has 75 vertices.

Original language	English
Pages (from-to)	211-215
Number of pages	5
Journal	Discrete Applied Mathematics
Volume	80
Issue number	2-3
DOIs	https://doi.org/10.1016/s0166-218x(97)88689-1
Publication status	Published - 11 Dec 1997
Externally published	Yes

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abstract = "Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Slater winner of T is the first vertex of any transitive tournament at minimum distance of T (the distance being the number of arcs to reverse in T to make T transitive). In this note, we show that there exists a tournament with 16 vertices for which no Slater winner is a Banks winner. This counterexample improves the previous one, due to G. Laffond and J.-F. Laslier, which has 75 vertices.",

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N2 - Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Slater winner of T is the first vertex of any transitive tournament at minimum distance of T (the distance being the number of arcs to reverse in T to make T transitive). In this note, we show that there exists a tournament with 16 vertices for which no Slater winner is a Banks winner. This counterexample improves the previous one, due to G. Laffond and J.-F. Laslier, which has 75 vertices.

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A 16-vertex tournament for which Banks set and Slater set are disjoint

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