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A parity domination problem in graphs with bounded treewidth and distance-hereditary graphs

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Abstract

This paper concerns a domination problem in graphs with parity constraints. The task is to find a subset of the vertices with minimum cost such that for every vertex the number of chosen vertices in its neighbourhood has a prespecified parity. This problem is known to be \({\mathcal NP}\) -hard for general graphs. A linear time algorithm was developed for series-parallel graphs and trees with unit cost and restricted to closed neighbourhoods. We present a linear time algorithm for the parity domination problem with open and closed neighbourhoods and arbitrary cost functions on graphs with bounded treewidth and distance-hereditary graphs.

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Authors and Affiliations

  1. Department of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria

    Elisabeth Gassner & Johannes Hatzl

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  1. Elisabeth Gassner
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  2. Johannes Hatzl
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Correspondence to Johannes Hatzl.

Additional information

This research is partially supported by the Austrian Science Fund Project P18918-N18 Efficiently solvable variants of location problems.

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Gassner, E., Hatzl, J. A parity domination problem in graphs with bounded treewidth and distance-hereditary graphs. Computing 82, 171–187 (2008). https://doi.org/10.1007/s00607-008-0005-8

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  • DOI: https://doi.org/10.1007/s00607-008-0005-8

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