Contracting planar graphs to contractions of triangulations

Marcin Kamiński, Daniël Paulusma, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. We identify a class of graphs C such that for every fixed H C, there exists a linear-time algorithm deciding whether a given planar graph G can be contracted to H. The class C is the closure of planar triangulated graphs under taking of contractions. In fact, we prove that a graph H C if and only if there exists a constant cH such that if the treewidth of a graph is at least cH, it contains H as a contraction. We also provide a characterization of C in terms of minimal forbidden contractions.

Original languageEnglish (US)
Pages (from-to)299-306
Number of pages8
JournalJournal of Discrete Algorithms
Issue number3
StatePublished - Sep 2011


  • Contraction
  • Dual graph
  • Fixed parameter tractable
  • Planar graph
  • Topological minor

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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