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

Florian Hörsch; Zoltán Szigeti

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

Combinatorics 2022-09-13 v2 Discrete Mathematics

Authors: Florian Hörsch , Zoltán Szigeti

Abstract

We show that the problem of deciding whether a given graph $G$ has a well-balanced orientation $\vec{G}$ such that $d_{\vec{G}}^+(v)\leq \ell(v)$ for all $v \in V(G)$ for a given function $\ell:V(G)\rightarrow \mathbb{Z}_{\geq 0}$ is NP-complete. We also prove a similar result for best-balanced orientations. This improves a result of Bern\' ath, Iwata, Kir\' aly, Kir\'aly and Szigeti and answers a question of Frank.

Keywords

graph orientation well-balanced orientation best-balanced orientation np-completeness out-degree bound graph theory

Cite

@article{arxiv.2202.13759,
  title  = {On the complexity of finding well-balanced orientations with upper bounds on the out-degrees},
  author = {Florian Hörsch and Zoltán Szigeti},
  journal= {arXiv preprint arXiv:2202.13759},
  year   = {2022}
}

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

Abstract

Keywords

Cite

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