## Acyclic orientations with degree constraints

### 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.

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}
}