Decomposing infinite matroids into their 3-connected minors

Elad Aigner-Horev, Reinhard Diestel, Luke Postle

Research output: Contribution to journalArticlepeer-review


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 vertices of T correspond to minors of M each of which is either a maximal 3-connected minor of M, a circuit or a cocircuit, and the edges of T correspond to certain 2-separations of M. In addition, we show that the decomposition of M determines the decomposition of its dual in a natural manner.

Original languageEnglish
Pages (from-to)11-16
Number of pages6
JournalElectronic Notes in Discrete Mathematics
StatePublished - 1 Dec 2011
Externally publishedYes


  • Decomposition trees
  • Infinite matroids
  • Matroid connectivity


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