On Seymour’s Second Neighborhood conjecture of [formula omitted]-free digraphs

Abstract

This paper gives an approximate result related to Seymour’s Second Neighborhood conjecture, that is, for any m-free digraph G, there exists a vertex v∈V(G) and a real number λm such that d++(v)≥λmd+(v), and λm→1 while m→+∞. This result generalizes and improves some known results in a sense.