The structure of 2-separations of infinite matroids

Elad Aigner-Horev, Reinhard Diestel, Luke Postle

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Generalizing a well known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits, and the edges of T correspond to certain nested 2-separations of M. These decompositions are invariant under duality.

Original languageEnglish
Pages (from-to)25-56
Number of pages32
JournalJournal of Combinatorial Theory. Series B
StatePublished - Jan 2016


  • 2-separation
  • 3-connected
  • Cunningham
  • Edmonds
  • Infinite
  • Matroid
  • Seymour
  • Tree-decomposition
  • Tutte


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