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

Authors:
Elisabeth Gassner;Johannes Hatzl
Affiliations:
Graz University of Technology, Department of Optimization and Discrete Mathematics, Steyrergasse 30, 8010, Graz, Austria;Graz University of Technology, Department of Optimization and Discrete Mathematics, Steyrergasse 30, 8010, Graz, Austria
Venue:
Computing
Year:
2008

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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.