TY - GEN

T1 - Minimization and parameterized variants of vertex partition problems on graphs

AU - Tamura, Yuma

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
Funding Yuma Tamura: Partially supported by JSPS KAKENHI Grant Number JP20J11259, Japan. Takehiro Ito: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. Xiao Zhou: Partially supported by JSPS KAKENHI Grant Number JP19K11813, Japan.
Publisher Copyright:
© Yuma Tamura, Takehiro Ito, and Xiao Zhou.

PY - 2020/12

Y1 - 2020/12

N2 - Let Π1, Π2, . . ., Πc be graph properties for a fixed integer c. Then, (Π1, Π2, . . ., Πc)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V1, V2, . . ., Vc such that the subgraph induced by Vi satisfies the graph property Πi for every i ∈ {1, 2, . . ., c}. Minimization and parameterized variants of (Π1, Π2, . . ., Πc)-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.

AB - Let Π1, Π2, . . ., Πc be graph properties for a fixed integer c. Then, (Π1, Π2, . . ., Πc)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V1, V2, . . ., Vc such that the subgraph induced by Vi satisfies the graph property Πi for every i ∈ {1, 2, . . ., c}. Minimization and parameterized variants of (Π1, Π2, . . ., Πc)-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.

KW - Approximability

KW - Feedback vertex set problem

KW - Fixed-parameter tractability

KW - Graph algorithms

KW - Vertex partition problem

UR - http://www.scopus.com/inward/record.url?scp=85100930242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85100930242&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2020.40

DO - 10.4230/LIPIcs.ISAAC.2020.40

M3 - Conference contribution

AN - SCOPUS:85100930242

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 401

EP - 4013

BT - 31st International Symposium on Algorithms and Computation, ISAAC 2020

A2 - Cao, Yixin

A2 - Cheng, Siu-Wing

A2 - Li, Minming

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 31st International Symposium on Algorithms and Computation, ISAAC 2020

Y2 - 14 December 2020 through 18 December 2020

ER -