License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.40
URN: urn:nbn:de:0030-drops-133844
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13384/
Go to the corresponding LIPIcs Volume Portal

Tamura, Yuma ; Ito, Takehiro ; Zhou, Xiao

Minimization and Parameterized Variants of Vertex Partition Problems on Graphs

pdf-format:
LIPIcs-ISAAC-2020-40.pdf (0.6 MB)

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
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI