## Packing countably many branchings with prescribed root-sets in digraphs without backward-infinite paths

### Abstract

We generalize an unpublished result of C. Thomassen. Let $D=(V,A)$ be a digraph without backward-infinite paths and let $\{ V_i \}_{i\in \mathbb{N}}$ be a multiset of subsets of $V$. We show that if all $v\in V$ is simultaneously reachable from the sets $V_i$ by edge-disjoint paths, then there exists a system of edge-disjoint spanning branchings $\{ \mathcal{B}_i \}_{i\in \mathbb{N}}$ in $D$ where the root-set of $\mathcal{B}_i$ is $V_i$.

Bibtex entry:

@techreport{egres-15-11,
AUTHOR = {Jo{\'o}, Attila},
TITLE = {Packing countably many branchings with prescribed root-sets in digraphs without backward-infinite paths},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2015},
NUMBER = {TR-2015-11}
}