Powers of paths in tournaments
Nemanja Draganić, François Dross, Jacob Fox, António Girão, Frédéric Havet, Dániel Korándi, William Lochet, David Munhá Correia, Alex Scott, Benny Sudakov · Combinatorics Probability Computing · 2021
Abstract 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.