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Disjoint paths in arborescences

By Livio Colussi, Michele Conforti and Giacomo Zambelli


An arborescence in a digraph is a tree directed away from its root. A classical theorem of Edmonds characterizes which digraphs have λ arc-disjoint arborescences rooted at r. A similar theorem of Menger guarantees that λ strongly arc disjoint rv-paths exist for every vertex v, where “strongly” means that no two paths contain a pair of symmetric arcs. We prove that if a directed graph D contains two arc-disjoint spanning arborescences rooted at r, then D contains two such arborences with the property that for every node v the paths from r to v in the two arborences satisfy Menger's theorem

Topics: QA Mathematics
Publisher: Elsevier
Year: 2005
DOI identifier: 10.1016/j.disc.2004.12.005
OAI identifier:
Provided by: LSE Research Online
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