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We give a necessary and sufficient condition for a graph to have an orientation that has $k$ edge-disjoint arborescences rooted at a designated vertex $s$ subject to lower and upper bounds on the in-degree at each vertex. The result is used to derive a characterization of graphs having a detachment that contains $k$ edge-disjoint spanning trees. Efficient algorithms for finding those orientations and detachments are also described. In particular, the paper provides an algorithm for finding a connected (loopless) detachment in $O(nm)$ time, improving on the previous best running time bound, where $n$ and $m$ denote the numbers of vertices and edges, respectively.
Bibtex entry:
AUTHOR | = | {Iwata, Satoru and Jord{\'a}n, Tibor}, |
TITLE | = | {Orientations and Detachments of Graphs with Prescribed Degrees and Connectivity}, |
NOTE | = | {{\tt egres.elte.hu}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2013}, |
NUMBER | = | {TR-2013-01} |