What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments

TL;DR

This paper explores the number of Hamilton cycles in tournaments, demonstrating that explicit constructions can have significantly more than the previously conjectured minimum, thus advancing understanding of tournament structures.

Contribution

The paper shows that explicit tournaments can contain more Hamilton cycles than previously believed, surpassing Moser's initial lower bound.

Findings

Explicit tournaments can have more than (rac{n}{3e})^n Hamilton cycles.

The results improve lower bounds on Hamilton cycles in tournaments.

Provides new constructions with many Hamilton cycles.

Abstract

Moser asked for a construction of explicit tournaments on $n$ vertices having at least $(\frac{n}{3e})^n$ Hamilton cycles. We show that he could have asked for rather more.