## Abstract Let __G__ be a graph and __T__ a set of vertices. A __Tβpath__ in __G__ is a path that begins and ends in __T__, and none of its internal vertices are contained in __T__. We define a __Tβpath covering__ to be a union of vertexβdisjoint __T__βpaths spanning all of __T__. Concentrating on
Disjoint Paths in Graphs III, Characterization
β Scribed by Xingxing Yu
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 326 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0218-0006
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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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