We generalize an unpublished result of C. Thomassen.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} |