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General vertex disjoint paths in series-parallel graphs

✍ Scribed by Ephraim Korach; Ady Tal

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
986 KB
Volume
41
Category
Article
ISSN
0166-218X

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A theorem of J. Edmonds states that a directed graph has k edge-disjoint branchings rooted at a vertex r if and only if every vertex has k edge-disjoint paths to r . We conjecture an extension of this theorem to vertex-disjoint paths and give a constructive proof of the conjecture in the case k = 2.

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## Abstract Let __G__ be a graph and __T__ a set of vertices. A __T‐path__ in __G__ is a path that begins and ends in __T__, and none of its internal vertices are contained in __T__. We define a __T‐path covering__ to be a union of vertex‐disjoint __T__‐paths spanning all of __T__. Concentrating on