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Zbl 0846.05040
Charon-Fournier, Irène; Germa, Anne; Hudry, Olivier
Bounds of Slater's index of a tournament from its scores. (Encadrement de l'indice de Slater d'un tournoi à l'aide de ses scores.) (French)
[J] Math. Inf. Sci. Hum. 118, 53-68 (1992). ISSN 0995-2314

Summary: We define a parameter $\sigma(T)$ from the scores of a tournament $T$. This parameter measures a remoteness between the tournament $T$ and the transitive tournaments of the same order. Calling $i(T)$ the minimum number of arcs to reverse to make $T$ transitive, we show the relation $\sigma(T)\le i(T)$. Then we give bounds on the maximum value of $i(T)$ for tournaments $T$ with given value of $\sigma$. Lastly, according to $\sigma(T)$ and the number of vertices of $T$, we deduce bounds of $i(T)$ for any tournament $T$.

MSC 2000:: *05C20 Directed graphs (digraphs)

Keywords: scores; tournament; bounds

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