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 α 1,α 2,...,α k for every α 1,α 2,...,α 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 α 1,α 2,...,α k for a given partition α 1,α 2,...,α k of the order of the graph, is NP-hard.
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© 2009 Springer-Verlag Berlin Heidelberg
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Broersma, H., Kratsch, D., Woeginger, G.J. (2009). Fully Decomposable Split Graphs. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_13
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DOI: https://doi.org/10.1007/978-3-642-10217-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10216-5
Online ISBN: 978-3-642-10217-2
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