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Article Dans Une Revue Journal of Combinatorial Optimization Année : 2023

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

Résumé

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.

Dates et versions

hal-03961401 , version 1 (28-01-2023)

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Florian Hörsch, Zoltán Szigeti. On the complexity of finding well-balanced orientations with upper bounds on the out-degrees. Journal of Combinatorial Optimization, 2023, 45 (1), pp.30. ⟨10.1007/s10878-022-00962-y⟩. ⟨hal-03961401⟩
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