language-icon Old Web
English
Sign In

Powers of paths in tournaments

2021 
In this short note we prove that every tournament contains the $k$-th power of a directed path of linear length. This improves upon recent results of Yuster and of Gir\~ao. We also give a complete solution for this problem when $k=2$, showing that there is always a square of a directed path of length $\lceil 2n/3 \rceil-1$, which is best possible.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    5
    References
    5
    Citations
    NaN
    KQI
    []