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A constructive solution to a problem of ranking tournaments

2019/02/18 by Shohei Satake, Satake, Shohei
Engineering · Computer Science · #graph theory and CDMA systems #Coding theory and cryptography #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.1902.10204

Abstract

A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erdős 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.

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