Acyclic orientations with degree constraints

Zoltán Király; Dömötör Pálvölgyi

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arXiv · 1806.03426

Acyclic orientations with degree constraints

Zoltán Király·Dömötör Pálvölgyi

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Abstract

In this note we study the complexity of some generalizations of the notion of $st$-numbering. Suppose that given some functions $f$ and $g$, we want to order the vertices of a graph such that every vertex $v$ is preceded by at least $f(v)$ of its neighbors and succeeded by at least $g(v)$ of its neighbors. We prove that this problem is solvable in polynomial time if $fg\equiv 0$, but it becomes NP-complete for $f\equiv g \equiv 2$. This answers a question of the first author posed in 2009.

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BibTeX RIS

Zoltán Király, Dömötör Pálvölgyi. 2018-06-09. Acyclic orientations with degree constraints. https://arxiv.org/abs/1806.03426

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