Fully decomposable split graphs

  • Authors:

  • Hajo Broersma;Dieter Kratsch;Gerhard J. Woeginger

  • Affiliations:

  • Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;LITA, Université Paul Verlaine-Metz, 57045 Metz Cedex 01, France;Department of Mathematics and Computer Science, TU Eindhoven, P.O.Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2013

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Abstract

We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, that is, whether it can be partitioned into connected parts of orders @a"1,@a"2,...,@a"k for every @a"1,@a"2,...,@a"k summing up to the order of the graph. In contrast, we show that the decision problem whether a given split graph can be partitioned into connected parts of orders @a"1,@a"2,...,@a"k for a given partition @a"1,@a"2,...,@a"k of the order of the graph, is NP-hard.