Pascal Gollin, Enlarging vertex-flames in countable digraphs

A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. A structural generalisation of vertex-flames and largeness to infinite digraphs was given by Joó and the analogue of Lovász’ result for countable digraphs was shown.

In this talk, I present a strengthening of this result stating that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame.

Joint work with Joshua Erde and Attila Joó.