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 -