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On partitioning a graph into two connected subgraphs.

Paulusma, Daniel and Rooij van, J.M.M. (2011) 'On partitioning a graph into two connected subgraphs.', Theoretical computer science., 412 (48). pp. 6761-6769.


Suppose a graph G is given with two vertex-disjoint sets of vertices Z1 and Z2. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z1 and Z2, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of n-vertex graphs G=(V,E) in which Z1 and Z2 each contain a connected set that dominates all vertices in V∖(Z1∪Z2). We present an O∗(1.2051n) time algorithm that solves it for this graph class. As a consequence, we can also solve this problem in O∗(1.2051n) time for the classes of n-vertex P6-free graphs and split graphs. This is an improvement upon a recent O∗(1.5790n) time algorithm for these two classes. Our approach translates the problem to a generalized version of hypergraph 2-coloring and combines inclusion/exclusion with measure and conquer.

Item Type:Article
Keywords:Disjoint connected subgraphs, Dominating set, Exact algorithm.
Full text:Full text not available from this repository.
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Record Created:07 Dec 2011 14:51
Last Modified:03 Apr 2013 16:20

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