On explicit random-like tournaments

TL;DR

This paper establishes a new theorem linking the quasi-random property of regular tournaments to their spectral characteristics, offering solutions to a longstanding construction problem posed by Erdős, Moon, and Spencer.

Contribution

It introduces a novel theorem connecting spectral properties with quasi-randomness in regular tournaments, advancing understanding in combinatorial design theory.

Findings

New theorem relating spectra and quasi-randomness

Solutions to classical construction problems in tournament design

Enhanced understanding of spectral properties in regular tournaments

Abstract

We give a new theorem describing a relation between the quasi-random property of regular tournaments and their spectra. This provides many solutions to a constructing problem mentioned by Erd\H{o}s and Moon (1965) and Spencer (1985).