## Abstract For an integer __l__β>β1, the __l__βedgeβconnectivity of a connected graph with at least __l__ vertices is the smallest number of edges whose removal results in a graph with __l__ components. A connected graph __G__ is (__k__, __l__)βedgeβconnected if the __l__βedgeβconnectivity of __G_
On k-minimally n-edge-connected graphs
β Scribed by Stephen B. Maurer; Peter J. Slater
- Book ID
- 107748285
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 815 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
A graph G = (V; E) is called minimally (k; T )-edge-connected with respect to some T β V if there exist k-edge-disjoint paths between every pair u; v β T but this property fails by deleting any edge of G. We show that |V | can be bounded by a (linear) function of k and |T | if each vertex in V -T ha
For a connected graph G = (V, E), an edge set S β E is a restricted edge cut if G -S is disconnected and there is no isolated vertex in G -S. The cardinality of a minimum restricted edge cut of G is the restricted edge connectivity of G, denoted by Ξ» (G). , where ΞΎ(G) is the minimum edge degree of
In this article, we deal with a connectivity problem stated by Maurer and Slater to characterize minimally k-edge'-connected graphs. This problem has been solved for k = 1,2 and 3, and we recall herein the results obtained. Then we give some partial results concerning the case k =4: representation o
## Abstract A constructive characterization of minimally 2βedge connected graphs, similar to those of Dirac for minimally 2βconnected graphs is given.