Geodesic
A note on arc-disjoint cycles in tournaments
Jan Florek1
1 Institute of Mathematics and Cybernetics University of Economics Komandorska 118/120 53-345 Wrocław, Poland
Colloquium Mathematicum, Tome 136 (2014) no. 2, pp. 259-262

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that every vertex $v$ of a tournament $T$ belongs to at least $$\max\{\min\{\delta ^+(T), 2\delta ^+(T) - d^+_T(v) +1\}, \min\{\delta ^-(T), 2\delta ^-(T) - d^-_T(v) +1\}\}$$ arc-disjoint cycles, where $\delta ^+(T)$ (or $\delta ^-(T)$) is the minimum out-degree (resp. minimum in-degree) of $T$, and $d^+_T(v)$ (or $d^-_T(v)$) is the out-degree (resp. in-degree) of $v$.
DOI : 10.4064/cm136-2-7
Keywords: prove every vertex nbsp tournament belongs least max min delta delta min delta delta arc disjoint cycles where delta delta minimum out degree resp minimum in degree out degree resp in degree

Jan Florek 1

1 Institute of Mathematics and Cybernetics University of Economics Komandorska 118/120 53-345 Wrocław, Poland 
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Jan Florek. A note on arc-disjoint cycles in tournaments. Colloquium Mathematicum, Tome 136 (2014) no. 2, pp. 259-262. doi: 10.4064/cm136-2-7

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