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The Parameterized Complexity of the Equidomination Problem

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Graph-Theoretic Concepts in Computer Science (WG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10520))

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Abstract

A graph \(G=(V,E)\) is called equidominating if there exists a value and a weight function such that the total weight of a subset \(D\subseteq V\) is equal to t if and only if D is a minimal dominating set. To decide whether or not a given graph is equidominating is referred to as the Equidomination problem.

In this paper we show that two parameterized versions of the Equidomination problem are fixed-parameter tractable: the first parameterization considers the target value t leading to the Target-t Equidomination problem. The second parameterization allows only weights up to a value k, which yields the k-Equidomination problem.

In addition, we characterize the graphs whose every induced subgraph is equidominating. We give a finite forbidden induced subgraph characterization and derive a fast recognition algorithm.

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Notes

  1. 1.

    http://arxiv.org/abs/1705.05599.

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Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Weyertal 80, 50931, Cologne, Germany

    Oliver Schaudt & Fabian Senger

Authors
  1. Oliver Schaudt
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  2. Fabian Senger
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Correspondence to Fabian Senger .

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Editors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany

    Gerhard J. Woeginger

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Schaudt, O., Senger, F. (2017). The Parameterized Complexity of the Equidomination Problem. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-68705-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68704-9

  • Online ISBN: 978-3-319-68705-6

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