TY - JOUR

T1 - Deletion to scattered graph classes I - Case of finite number of graph classes

AU - Jacob, Ashwin

AU - de Kroon, Jari J.H.

AU - Majumdar, Diptapriyo

AU - Raman, Venkatesh

N1 - Funding Information:
A preliminary version of the paper appeared in proceedings of IPEC 2020. The second author has received funding from the European Research Council (ERC) under the European Union's Horizon2020 research and innovation programme (grant agreement No 803421, ReduceSearch).The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Jari J.H. de Kroon reports financial support was provided by European Research Council under the European Union's Horizon2020 research and innovation programme (grant agreement No 803421, ReduceSearch).
Funding Information:
A preliminary version of the paper appeared in proceedings of IPEC 2020. The second author has received funding from the European Research Council (ERC) under the European Union's Horizon2020 research and innovation programme (grant agreement No 803421 , ReduceSearch).
Publisher Copyright:
© 2023 Elsevier Inc.

PY - 2023/12/1

Y1 - 2023/12/1

N2 - Graph-deletion problems involve deleting a small number of vertices so that the resulting graph belong to a given hereditary graph class. We initiate a study of a natural variation of the problem of deletion to scattered graph classes. We want to delete at most k vertices so that each connected component of the resulting graph belongs to one of the constant number of graph classes. As our main result, we show that this problem is non-uniformly fixed-parameter tractable (FPT) when the deletion problem corresponding to each of the constant number of graph classes is known to be FPT and the properties that a graph belongs to these classes are expressible in Counting Monodic Second Order (CMSO) logic. While this is shown using some black box theorems in parameterized complexity, we give a faster FPT algorithm when each of the graph classes has a finite forbidden set.

AB - Graph-deletion problems involve deleting a small number of vertices so that the resulting graph belong to a given hereditary graph class. We initiate a study of a natural variation of the problem of deletion to scattered graph classes. We want to delete at most k vertices so that each connected component of the resulting graph belongs to one of the constant number of graph classes. As our main result, we show that this problem is non-uniformly fixed-parameter tractable (FPT) when the deletion problem corresponding to each of the constant number of graph classes is known to be FPT and the properties that a graph belongs to these classes are expressible in Counting Monodic Second Order (CMSO) logic. While this is shown using some black box theorems in parameterized complexity, we give a faster FPT algorithm when each of the graph classes has a finite forbidden set.

KW - Fixed parameter tractability

KW - Important separators

KW - Parameterized complexity

KW - Scattered graph classes

UR - http://www.scopus.com/inward/record.url?scp=85163554515&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2023.05.005

DO - 10.1016/j.jcss.2023.05.005

M3 - Article

AN - SCOPUS:85163554515

SN - 0022-0000

VL - 138

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

M1 - 103460

ER -