2013/09/15 by Nathan Bowler, Bowler, Nathan, Johannes Carmesin +3 · 2 citations
Computer Science · Engineering · Mathematics · #05B35 #05C63 #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Interconnection Networks and Systems #graph theory and CDMA systems #math.CO #msc:05B35 #msc:05C63
paper · pdf · doi:10.48550/arxiv.1309.3735
arxiv created 2013/09/15 · openalex publication_date 2013/09/15 · arxiv updated 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.