2026-08-16T14:49:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13384 2024-03-06T10:51:51Z ddc:004 open_access

Minimization and Parameterized Variants of Vertex Partition Problems on Graphs Tamura, Yuma Ito, Takehiro Zhou, Xiao Graph Algorithms Approximability Fixed-Parameter Tractability Vertex Partition Problem Feedback Vertex Set Problem 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yuma Tamura and Takehiro Ito and Xiao Zhou 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.40 urn:nbn:de:0030-drops-133844 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.40 eng https://creativecommons.org/licenses/by/3.0/legalcode