By a well-known theorem of Edmonds if a finite digraph is $k$-edge-connected from vertex $r$ then it has $k$ edge-disjoint spanning arborescences rooted at $r$. As it was shown by R. Aharoni and C. Thomassen, this does not remain true for infinite digraphs. Thomassen also proved that for the class of digraphs without backward-infinite paths the above theorem of Edmonds remains true. Our main result is that for digraphs without forward-infinite paths the theorem is also true, even in general form.
Bibtex entry:
@techreport{egres-14-13,
AUTHOR | = | {Jo{\'o}, Attila}, |
TITLE | = | {Edmonds' Branching Theorem in Digraphs without Forward-infinite Paths}, |
NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2014}, |
NUMBER | = | {TR-2014-13} |