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.

Bibtex entry:

@techreport{egres-18-07,

AUTHOR | = | {Kir{\'a}ly, Zolt{\'a}n and P{\'a}lvölgyi, Dömötör}, |

TITLE | = | {Acyclic orientations with degree constraints}, |

NOTE | = | {{\tt www.cs.elte.hu/egres}}, |

INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |

YEAR | = | {2018}, |

NUMBER | = | {TR-2018-07} |