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NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrary, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and Müller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter "maximum degree".

preprint2012arXivOpen access
Sepp HartungAndré Nichterlein
Computational Complexity
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Sepp HartungAndré Nichterlein

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