A constructive solution to a problem of ranking tournaments
Combinatorics
2019-02-28 v1
Abstract
A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they also mentioned the problem of explicit constructions. However, there seems to be only a few of explicit constructions of such tournaments. In this note, we give a construction of many such tournaments by using skew Hadamard difference sets which have been investigated in combinatorial design theory.
Cite
@article{arxiv.1902.10204,
title = {A constructive solution to a problem of ranking tournaments},
author = {Shohei Satake},
journal= {arXiv preprint arXiv:1902.10204},
year = {2019}
}
Comments
7 pages. arXiv admin note: text overlap with arXiv:1901.10733