## Abstract We consider finite undirected loopless graphs __G__ in which multiple edges are possible. For integers k,l ≥ 0 let g(k, l) be the minimal __n__ ≥ 0 with the following property: If __G__ is an __n__‐edge‐connected graph, __s__~1~, ⃛,__s__~k~, __t__~1~, ⃛,__t__~k~ are vertices of __G__, a
Short Disjoint Paths in Locally Connected Graphs
✍ Scribed by Chuanping Chen; Roman Čada; Tomáš Kaiser; Zdeněk Ryjáček
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 185 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
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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
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.