Containment relations in split graphs

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

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
• Electronic ISSN: 1872-6771
• 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