A note on 2-vertex-connected orientations

12/14/2021

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by   Florian Hörsch, et al.

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We consider two possible extensions of a theorem of Thomassen characterizing the graphs admitting a 2-vertex-connected orientation. First, we show that the problem of deciding whether a mixed graph has a 2-vertex-connected orientation is NP-hard. This answers a question of Bang-Jensen, Huang and Zhu. For the second part, we call a directed graph D=(V,A) 2T-connected for some T ⊆ V if D is 2-arc-connected and D-v is strongly connected for all v ∈ T. We deduce a characterization of the graphs admitting a 2T-connected orientation from the theorem of Thomassen.