NP-Hardness and fixed-parameter tractability of realizing degree sequences with directed acyclic graphs

  • Authors:

  • Sepp Hartung;André Nichterlein

  • Affiliations:

  • Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin, Germany

  • Venue:
  • CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
  • Year:
  • 2012

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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 the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrast, 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".