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 egres.elte.hu}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2018}, |
NUMBER | = | {TR-2018-07} |