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DOI: 10.4230/LIPIcs.ISAAC.2020.40
URN: urn:nbn:de:0030-drops-133844
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13384/
Tamura, Yuma ; Ito, Takehiro ; Zhou, Xiao
Minimization and Parameterized Variants of Vertex Partition Problems on Graphs
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Abstract
Let Π₁, Π₂, …, Π_c be graph properties for a fixed integer c. Then, (Π₁, Π₂, …, Π_c)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V₁, V₂, …, V_c such that the subgraph induced by V_i satisfies the graph property Π_i for every i ∈ {1,2, …, c}. Minimization and parameterized variants of (Π₁, Π₂, …, Π_c)-Partition have been studied for several specific graph properties, where the size of the vertex subset V₁ satisfying Π₁ is minimized or taken as a parameter. In this paper, we first show that the minimization variant is hard to approximate for any nontrivial additive hereditary graph properties, unless c = 2 and both Π₁ and Π₂ are classes of edgeless graphs. We then give FPT algorithms for the parameterized variant when restricted to the case where c = 2, Π₁ is a hereditary graph property, and Π₂ is the class of acyclic graphs.
BibTeX - Entry
@InProceedings{tamura_et_al:LIPIcs:2020:13384,
author = {Yuma Tamura and Takehiro Ito and Xiao Zhou},
title = {{Minimization and Parameterized Variants of Vertex Partition Problems on Graphs}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {40:1--40:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-173-3},
ISSN = {1868-8969},
year = {2020},
volume = {181},
editor = {Yixin Cao and Siu-Wing Cheng and Minming Li},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13384},
URN = {urn:nbn:de:0030-drops-133844},
doi = {10.4230/LIPIcs.ISAAC.2020.40},
annote = {Keywords: Graph Algorithms, Approximability, Fixed-Parameter Tractability, Vertex Partition Problem, Feedback Vertex Set Problem}
}
| Keywords: | Graph Algorithms, Approximability, Fixed-Parameter Tractability, Vertex Partition Problem, Feedback Vertex Set Problem | |
| Seminar: | 31st International Symposium on Algorithms and Computation (ISAAC 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
