Containment relations in split graphs

Golovach, P.A.; Kaminski, M.; Paulusma, D.; Thilikos, D.M.

doi:10.1016/j.dam.2011.10.004

Containment relations in split graphs

Golovach, P.A.; Kaminski, M.; Paulusma, D.; Thilikos, D.M.

Authors

P.A. Golovach

M. Kaminski

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

D.M. Thilikos

Abstract

A graph containment problem is to decide whether one graph can be modified into some other graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible graph operations permitted. By allowing any combination of these four operations we capture the following ten problems: testing on (induced) minors, (induced) topological minors, (induced) subgraphs, (induced) spanning subgraphs, dissolutions and contractions. A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. Our results combined with existing results settle the parameterized complexity of all ten problems for split graphs.

Citation

Golovach, P., Kaminski, M., Paulusma, D., & Thilikos, D. (2012). Containment relations in split graphs. Discrete Applied Mathematics, 160(1-2), 155-163. https://doi.org/10.1016/j.dam.2011.10.004

Journal Article Type	Article
Publication Date	Jan 1, 2012
Deposit Date	Dec 6, 2011
Journal	Discrete Applied Mathematics
Print ISSN	0166-218X
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	160
Issue	1-2
Pages	155-163
DOI	https://doi.org/10.1016/j.dam.2011.10.004
Keywords	Subgraph, Minor, Topological minor, Contraction.
Public URL	https://durham-repository.worktribe.com/output/1533549