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1

Menger’s theorem

1   Introduction

2   Vertex-connectivity

3   Edge-connectivity

4   Mixed connectivity

5   Average connectivity

6   Menger results for paths of bounded length

7   Connectivity of sets

8   Connecting with trees

References

In its best-known version, Menger’s theorem states that the maximum number of pairwise internally disjoint paths between a given pair of non-adjacent vertices in a graph equals the minimum number of vertices whose deletion disconnects the pair. Thus, the maximum number of pairwise internally disjoint paths that connect a given pair of vertices is a local measure that indicates how well two given vertices are connected. The connectivity of a graph is the minimum number of vertices whose ...

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