Abstract
The cluster vertex deletion number of a graph is the minimum number of its vertices whose deletion results in a disjoint union of complete graphs. This generalizes the vertex cover number, provides an upper bound to the clique-width and is related to the previously studied notion of the twin cover of the graph under consideration. We study the fixed parameter tractability of basic graph theoretic problems related to coloring and Hamiltonicity parameterized by cluster vertex deletion number. Our results show that most of these problems remain fixed parameter tractable as well, and thus we push the borderline between tractability and intractability towards the clique-width parameter.
Supported by Czech Research grants CE-ITI GAČR P202/12/6061 and GAUK 64110.
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Doucha, M., Kratochvíl, J. (2012). Cluster Vertex Deletion: A Parameterization between Vertex Cover and Clique-Width. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_32
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DOI: https://doi.org/10.1007/978-3-642-32589-2_32
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