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

Florian Hörsch () and Zoltán Szigeti
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Florian Hörsch: TU Ilmenau: Technische Universitat Ilmenau
Zoltán Szigeti: University Grenoble Alpes, Grenoble INP, Laboratory G-SCOP

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 36, 14 pages

Abstract: Abstract We show that the problem of deciding whether a given graph G has a well-balanced orientation $$\vec {G}$$ G → such that $$d_{\vec {G}}^+(v)\le \ell (v)$$ d G → + ( v ) ≤ ℓ ( v ) for all $$v \in V(G)$$ v ∈ V ( G ) for a given function $$\ell :V(G)\rightarrow \mathbb {Z}_{\ge 0}$$ 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.

Keywords: Graph orientation; Well-balanced; Complexity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00962-y

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