Minimum 2-edge strongly biconnected spanning directed subgraph problem

07/07/2022

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by   Raed Jaberi, et al.

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Wu and Grumbach introduced the concept of strongly biconnected directed graphs. A directed graph G=(V,E) is called strongly biconnected if the directed graph G is strongly connected and the underlying undirected graph of G is biconnected. A strongly biconnected directed graph G=(V,E) is said to be 2- edge strongly biconnected if it has at least three vertices and the directed subgraph (V,E∖{ e} ) is strongly biconnected for all e ∈ E. Let G=(V,E) be a 2-edge-strongly biconnected directed graph. In this paper we study the problem of computing a minimum size subset H ⊆ E such that the directed subgraph (V,H) is 2- edge strongly biconnected.