Packing cycles through prescribed vertices

Naonori Kakimura, Ken ichi Kawarabayashi, Dániel Marx

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


The well-known theorem of Erdo{double acute accent}s and Pósa says that a graph G has either k vertex-disjoint cycles or a vertex set X of order at most f(k) such that G\X is a forest. Starting with this result, there are many results concerning packing and covering cycles in graph theory and combinatorial optimization. In this paper, we generalize Erdo{double acute accent}s-Pósa's result to cycles that are required to go through a set S of vertices. Given an integer k and a vertex subset S (possibly unbounded number of vertices) in a given graph G, we prove that either G has k vertex-disjoint cycles, each of which contains at least one vertex of S, or G has a vertex set X of order at most f(k)=40k2log2k such that G\X has no cycle that intersects S.

Original languageEnglish
Pages (from-to)378-381
Number of pages4
JournalJournal of Combinatorial Theory. Series B
Issue number5
Publication statusPublished - 2011 Sept
Externally publishedYes


  • Disjoint cycles
  • Erdo{double acute accent}s-Pósa property
  • Feedback vertex sets

ASJC Scopus subject areas

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


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