An Overview of Quasirandomness: From Random Graphs and Random Tournaments to Uniformly Biased Tournaments

Abstract

This paper can be divided into two parts. In the first half, we provide an overview of quasirandom graphs and quasirandom tournaments, borrowing primarily from the work of Chung, Graham, and Wilson. In the second half, we consider uniformly biased tournament. By applying methods similar to those used by Chung, Graham, and Wilson, in conjunction with an appeal to a regularity argument, we prove the equivalence of three quasirandom properties for uniformly biased tournaments.