Upper bounds on the size of transitive subtournaments in digraphs

TL;DR

This paper establishes upper bounds on the size of transitive subtournaments in directed graphs, extending Hoffman's bound and improving it for specific classes like doubly regular tournaments using advanced algebraic techniques.

Contribution

It introduces a Hoffman's bound analogy for digraphs and enhances bounds for doubly regular tournaments with novel algebraic methods.

Findings

Derived an Hoffman's bound analogue for digraphs.

Improved bounds for doubly regular tournaments.

Applied block intersection polynomials in a new context.

Abstract

In this paper, we consider upper bounds on the size of transitive subtournaments in a digraph. In particular, we give an analogy of Hoffman's bound for the size of cocliques in a regular graph. Furthermore, we partially improve the Hoffman type bound for doubly regular tournaments by using the technique of Greaves and Soicher for strongly regular graphs [4], which gives a new application of block intersection polynomials.