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Journal of Combinatorial Optimization

Erschienen in:

01.07.2016

A complexity dichotomy and a new boundary class for the dominating set problem

verfasst von: D. S. Malyshev

Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2016

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Abstract

We study the computational complexity of the dominating set problem for hereditary graph classes, i.e., classes of simple unlabeled graphs closed under deletion of vertices. Every hereditary class can be defined by a set of its forbidden induced subgraphs. There are numerous open cases for the complexity of the problem even for hereditary classes with small forbidden structures. We completely determine the complexity of the problem for classes defined by forbidding a five-vertex path and any set of fragments with at most five vertices. Additionally, we also prove polynomial-time solvability of the problem for some two classes of a similar type. The notion of a boundary class is a helpful tool for analyzing the computational complexity of graph problems in the family of hereditary classes. Three boundary classes were known for the dominating set problem prior to this paper. We present a new boundary class for it.

Vorheriger Artikel New analysis and computational study for the planar connected dominating set problem

Nächster Artikel 2-Distance coloring of a planar graph without 3, 4, 7-cycles

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Titel: A complexity dichotomy and a new boundary class for the dominating set problem
verfasst von: D. S. Malyshev
Publikationsdatum: 01.07.2016
Verlag: Springer US
Erschienen in: Journal of Combinatorial Optimization / Ausgabe 1/2016
Print ISSN: 1382-6905
Elektronische ISSN: 1573-2886
DOI: https://doi.org/10.1007/s10878-015-9872-z

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