Fully decomposable split graphs


Broersma, Hajo and Kratsch, Dieter and Woeginger, Gerhard J. (2009) Fully decomposable split graphs. In: 20th International Workshop on Combinatorial Algorithms, IWOCA 2009, June 28 - July 2 2009, Hradec nad Moravicí, Czech Republic (pp. pp. 105-112).

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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 $\alpha_1,\alpha_2,\dots, \alpha_k$ for every $\alpha_1,\alpha_2,\ldots,\alpha_k$ 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 $\alpha_1,\alpha_2,\ldots,\alpha_k$ for a given partition $\alpha_1,\alpha_2,\ldots,\alpha_k$ of the order of the graph, is NP-hard.
Item Type:Conference or Workshop Item
Copyright:© 2009 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/71247
Official URL:https://doi.org/10.1007/978-3-642-10217-2_13
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