Powers of paths in tournaments
Combinatorics
2021-02-17 v4
Abstract
In this short note we prove that every tournament contains the -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 , showing that there is always a square of a directed path of length , which is best possible.
Cite
@article{arxiv.2010.05735,
title = {Powers of paths in tournaments},
author = {Nemanja Draganić and François Dross and Jacob Fox and António Girão and Frédéric Havet and Dániel Korándi and William Lochet and David Munhá Correia and Alex Scott and Benny Sudakov},
journal= {arXiv preprint arXiv:2010.05735},
year = {2021}
}
Comments
6 pages; updated affiliations; accepted at CPC