Containment relations in split graphs

Petr A. Golovach, Marcin Kamiski, Danil Paulusma, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)155-163
Number of pages9
JournalDiscrete Applied Mathematics
Issue number1-2
StatePublished - Jan 2012


  • Contraction
  • Minor
  • Subgraph
  • Topological minor

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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