A 2O(k)n algorithm for k-cycle in minor-closed graph families

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Let C be a proper minor-closed family of graphs. We present a randomized algorithm that given a graph G∈C with n vertices, finds a simple cycle of size k in G (if exists) in 2O(k)n time. The algorithm applies to both directed and undirected graphs. In previous linear time algorithms for this problem, the runtime dependence on k is super-exponential. The algorithm can be derandomized yielding a 2O(k)nlog⁡n time algorithm.

Original languageEnglish
Pages (from-to)74-85
Number of pages12
JournalTheoretical Computer Science
StatePublished - 24 Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Linear time algorithm
  • Minor-closed graph family
  • Parameterized algorithm
  • k-cycle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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