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

Sepp Hartung; André Nichterlein

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arXiv · 1110.1510

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

Sepp Hartung·André Nichterlein

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Abstract

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".

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BibTeX RIS

Sepp Hartung, André Nichterlein. 2012-01-17. NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs. https://arxiv.org/abs/1110.1510

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