On the intersection of infinite matroids

Elad Aigner-Horev*, Johannes Carmesin, Jan Oliver Fröhlich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009. We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids. In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.

Original languageEnglish
Pages (from-to)1582-1596
Number of pages15
JournalDiscrete Mathematics
Issue number6
Early online date20 Mar 2018
Publication statusPublished - 1 Jun 2018


  • Infinite graphs
  • Infinite matroids
  • Matroid intersection

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'On the intersection of infinite matroids'. Together they form a unique fingerprint.

Cite this