Infinite graphic matroids

Nathan Bowler, Johannes Carmesin, Robin Christian

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graph-like topological space: that is, a graph-like space in the sense of Thomassen and Vella. This extends Tutte's characterization of finite graphic matroids. The representation we construct has many pleasant topological properties. Working in the representing space, we prove that any circuit in a 3-connected graphic matroid is countable.
Original languageEnglish
Pages (from-to)305–339
Number of pages35
Issue number2
Early online date27 Mar 2018
Publication statusPublished - Apr 2018


  • math.CO
  • 05B35
  • 05C63


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