Catalan structures and dynamic programming in H-minor-free graphs

Frederic Dorn, Fedor V. Fomin, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


We give an algorithm that, for a fixed graph H and integer k, decides whether an n-vertex H-minor-free graph G contains a path of length k in 2 O(k)nO(1) steps. Our approach builds on a combination of Demaine-Hajiaghayis bounds on the size of an excluded grid in such graphs with a novel combinatorial result on certain branch decompositions of H-minor-free graphs. This result is used to bound the number of ways vertex disjoint paths can be routed through the separators of such decompositions. The proof is based on several structural theorems from the Graph Minors series of Robertson and Seymour. With a slight modification, similar combinatorial and algorithmic results can be derived for many other problems. Our approach can be viewed as a general framework for obtaining time 2O(k)nO(1) algorithms on H-minor-free graph classes.

Original languageEnglish (US)
Pages (from-to)1606-1622
Number of pages17
JournalJournal of Computer and System Sciences
Issue number5
StatePublished - Sep 2012


  • Catalan structure
  • Longest path
  • Minor-free graphs
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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