Leírás
In the finite case an r-vertex-flame is a finite directed graph
F with r\in V(F) in which for every vertex v\neq r
the indegree of v is equal to \kappa_F(r,v) (the local connectivity from r to v in F).
G. Calvillo Vives proved that if D is a finite directed graph with r\in V(D),
then there is a spanning subdigraph F of D such that F is an r-vertex-flame and
\kappa_F(r,v)=\kappa_D(r,v) holds for every v. Our goal is to find the ``right'' infinite generalization of this theorem. We
extend the definition of flame to the infinite case by demanding for every v an internally disjoint system of r\rightarrow v paths which
uses all the ingoing edges of v. Instead of just preserving the local connectivities from r as cardinals we want to preserve in F
for every v an Aharoni-Berger cut of D from r to v. The main result is to accomplish this for countable digraphs.