Domination and fractional domination in digraphs (Q1671654)

Summary: 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 \(G\) on \(n\) vertices has fractional domination number at most \(2\alpha(G)\) and domination number at most \(2\alpha(G) \cdot \log{n}\). Both bounds are sharp.