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Powers of paths in tournaments

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 Girão. 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 , w...

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Main Authors: Draganić, Nemanja (Author) , Dross, François (Author) , Fox, Jacob (Author) , Girao, Antonio (Author) , Havet, Frédéric (Author) , Korándi, Dániel (Author) , Lochet, William (Author) , Correia, David Munhá (Author) , Scott, Alex (Author) , Sudakov, Benny (Author)
Format: Article (Journal)
Language:English
Published: 23 March 2021
In: Combinatorics, probability & computing
Year: 2021, Volume: 30, Issue: 6, Pages: 894-898
ISSN:1469-2163
DOI:10.1017/S0963548321000067
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1017/S0963548321000067
Verlag, lizenzpflichtig, Volltext: https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/powers-of-paths-in-tournaments/3CA48CC1DB5AA4C7A2BB4F9F056A6933
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Author Notes:Nemanja Draganić, François Dross, Jacob Fox, António Girão, Frédéric Havet, Dániel Korándi, William Lochet, David Munhá Correia, Alex Scott and Benny Sudakov
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Summary: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 Girão. 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 , which is best possible.
Item Description:Gesehen am 04.05.2022
Physical Description:Online Resource
ISSN:1469-2163
DOI:10.1017/S0963548321000067

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