PINLOU , Alexandre

In a directed graph, a star is an arborescence with at least one arc, in which the root dominates all the other vertices. A galaxy is a vertex-disjoint union of stars. In this paper, we consider the Spanning Galaxy problem of deciding whether a digraph D has a spanning galaxy or not. We show that although this problem is NP-complete (even...

A star is an arborescence in which the root dominates all the other vertices. A galaxy is a vertex-disjoint union of stars. The directed star arboricity of a digraph D, denoted by dst(D), is the minimum number of galaxies needed to cover A(D). In this paper, we show that dst(D)less-than-or-equals, slantΔ(D)+1 and that if D is acyclic then...