Fully Decomposable Split Graphs

  • Authors:

  • Hajo Broersma;Dieter Kratsch;Gerhard J. Woeginger

  • Affiliations:

  • Department of Computer Science, Durham University, Science Laboratories, Durham, England DH1 3LE;LITA, Université de Metz, Metz Cedex 01, France 57045;Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, The Netherlands 5600

  • Venue:
  • Combinatorial Algorithms
  • Year:
  • 2009

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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, i.e., whether it can be partitioned into connected parts of order 驴 1,驴 2,...,驴 k for every 驴 1,驴 2,...,驴 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 order 驴 1,驴 2,...,驴 k for a given partition 驴 1,驴 2,...,驴 k of the order of the graph, is NP-hard.