Acyclic orientations with degree constraints

06/09/2018

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by   Zoltán Király, et al.

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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≡ 0, but it becomes NP-complete for f≡ g ≡ 2. This answers a question of the first author posed in 2009.