From Few Components to an Eulerian Graph by Adding Arcs

  • Manuel Sorge
  • René van Bevern
  • Rolf Niedermeier
  • Mathias Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)


Eulerian Extension (EE) is the problem to make an arc-weighted directed multigraph Eulerian by adding arcs of minimum total cost. EE is NP-hard and has been shown fixed-parameter tractable with respect to the number of arc additions. Complementing this result, on the way to answering an open question, we show that EE is fixed-parameter tractable with respect to the combined parameter “number of connected components in the underlying undirected multigraph” and “sum of indeg(v) - outdeg(v) over all vertices v in the input multigraph where this value is positive.” Moreover, we show that EE is unlikely to admit a polynomial-size problem kernel for this parameter combination and for the parameter “number of arc additions”.


Weight Function Initial Vertex Terminal Vertex Input Instance Positive Balance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manuel Sorge
    • 1
  • René van Bevern
    • 1
  • Rolf Niedermeier
    • 1
  • Mathias Weller
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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