Further hardness results on the generalized connectivity of graphs

The generalized $k$-connectivity $κ_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984, which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we determine the computational complexity of the generalized connectivity and generalized edge-connectivity of a graph. Two conjectures are also proved to be true.

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