Edge-Editing to a Dense and a Sparse Graph Class

KOTRBČÍK, Michal, Rastislav KRÁLOVIČ and Sebastian ORDYNIAK. Edge-Editing to a Dense and a Sparse Graph Class. In Kranakis E., Navarro G., Chávez E. LATIN 2016: Latin American Symposium on Theoretical Informatics. Berlin: Springer, 2016, p. 562-575. ISBN 978-3-662-49528-5. Available from: https://dx.doi.org/10.1007/978-3-662-49529-2_42.

Basic information

• Original name: Edge-Editing to a Dense and a Sparse Graph Class
• Authors: KOTRBČÍK, Michal (703 Slovakia, guarantor, belonging to the institution), Rastislav KRÁLOVIČ (703 Slovakia) and Sebastian ORDYNIAK (276 Germany).
• Edition: Berlin, LATIN 2016: Latin American Symposium on Theoretical Informatics, p. 562-575, 14 pp. 2016.
• Publisher: Springer

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: Germany
• Confidentiality degree: is not subject to a state or trade secret
• Publication form: printed version "print"
• Impact factor: Impact factor: 0.402 in 2005
• RIV identification code: RIV/00216224:14330/16:00094278
• Organization unit: Faculty of Informatics
• ISBN: 978-3-662-49528-5
• ISSN: 0302-9743
• Doi: http://dx.doi.org/10.1007/978-3-662-49529-2_42
• Keywords in English: Clique-editing; Degeneracy; Graph modification problems; Parameterized complexity; Treewidth
• Tags: firank_B
• Tags: International impact, Reviewed

Abstract

We consider a graph edge-editing problem, where the goal is to transform a given graph G into a disjoint union of two graphs from a pair of given graph classes, investigating what properties of the classes make the problem fixed-parameter tractable. We focus on the case when the first class is dense, i.e. every such graph G has minimum degree at least |V (G)| - delta for a constant delta, and assume that the cost of editing to this class is fixed-parameter tractable parameterized by the cost. Under the assumptions that the second class either has bounded maximum degree, or is edge-monotone, can be defined in MSO2, and has bounded treewidth, we prove that the problem is fixed-parameter tractable parameterized by the cost. We also show that the problem is fixed-parameter tractable parameterized by degeneracy if the second class consists of independent sets and Subgraph Isomorphism is fixedparameter tractable for the input graphs. On the other hand, we prove that parameterization by degeneracy is in general W[1]-hard even for editing to cliques and independent sets.