On the complexity of finding well-balanced orientations with upper bounds on the out-degrees

02/28/2022

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by   Florian Hörsch, et al.

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We show that the problem of deciding whether a given graph G has a well-balanced orientation G⃗ such that d_G⃗^+(v)≤ℓ(v) for all v ∈ V(G) for a given function ℓ:V(G)→ℤ_≥ 0 is NP-complete. We also prove a similar result for best-balanced orientations. This improves a result of Bernáth, Iwata, Király, Király and Szigeti and answers a question of Frank.