A+ CATEGORY SCIENTIFIC UNIT

A note on arc-disjoint cycles in tournaments

Volume 136 / 2014

Jan Florek Colloquium Mathematicum 136 (2014), 259-262 MSC: 05C20, 05C35, 05C38. DOI: 10.4064/cm136-2-7

Abstract

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 $v$.

Authors

  • Jan FlorekInstitute of Mathematics and Cybernetics
    University of Economics
    Komandorska 118/120
    53-345 Wrocław, Poland
    e-mail

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