A note on arc-disjoint cycles in tournaments
Tom 136 / 2014
Colloquium Mathematicum 136 (2014), 259-262
MSC: 05C20, 05C35, 05C38.
DOI: 10.4064/cm136-2-7
Streszczenie
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 $v$.
