The maximum edge-disjoint paths problem in complete graphs
β Scribed by Adrian Kosowski
- Book ID
- 108281412
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 426 KB
- Volume
- 399
- Category
- Article
- ISSN
- 0304-3975
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π SIMILAR VOLUMES
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.
## Abstract We consider finite undirected loopless graphs __G__ in which multiple edges are possible. For integers k,l β₯ 0 let g(k, l) be the minimal __n__ β₯ 0 with the following property: If __G__ is an __n__βedgeβconnected graph, __s__~1~, β,__s__~k~, __t__~1~, β,__t__~k~ are vertices of __G__, a
GivenanodesandasetZ'={t~,..., tk} of k nodes in a k-connected graph, the node-to-set disjoint paths problem is to find k node-disjoint paths pi : s -+ ti, 1 < i < k. In this paper, we give two O(n\*) time algorithms for the node-to-set disjoint paths problem in n-dimensional star graphs G, which are