Edge and vertex intersection of paths in a tree
โ Scribed by Martin Charles Golumbic; Robert E. Jamison
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 572 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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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.
## Abstract Let ${\cal G}^{s}\_{r}$ denote the set of graphs with each vertex of degree at least __r__ and at most __s__, __v__(__G__) the number of vertices, and ฯ~__k__~ (__G__) the maximum number of disjoint __k__โedge trees in __G__. In this paper we show that if __G__ โ ${\cal G}^{s}\_{2}$ a