Upper bounds on the size of transitive subtournaments in digraphs

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.In this paper, we consider analogies of the Hoffman bound and the Greaves-Soicher bound to digraphs. In particular, as an analogy of the Hoffman bound for regular graphs, we show that if a