Domination and fractional domination in digraphs

Abstract

In this paper, we investigate the relation between the (fractional) domination number of a digraph $G$ and the independence number of its underlying graph, denoted by $\alpha (G)$. More precisely, we prove that every digraph $G$ has fractional domination number at most $2\alpha (G)$, and every directed triangle-free digraph $G$ has domination number at most $\alpha (G)\cdot \alpha (G)!$. The first bound is sharp.

11 pages, no figure