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Journal Articles Combinatorics, Probability and Computing Year : 2021

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, which is best possible.
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hal-03269230 , version 1 (10-11-2021)



Nemanja Draganić, François Dross, Jacob Fox, António Girão, Frédéric Havet, et al.. Powers of paths in tournaments. Combinatorics, Probability and Computing, 2021, pp.1-5. ⟨10.1017/S0963548321000067⟩. ⟨hal-03269230⟩
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