From few components to an eulerian graph by adding arcs

  • Authors:

  • Manuel Sorge;René van Bevern;Rolf Niedermeier;Mathias Weller

  • Affiliations:

  • Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

  • Venue:
  • WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2011

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Abstract

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".