Infinite graphic matroids Part I
Combinatorics
2013-09-17 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1309.3735,
title = {Infinite graphic matroids Part I},
author = {Nathan Bowler and Johannes Carmesin and Robin Christian},
journal= {arXiv preprint arXiv:1309.3735},
year = {2013}
}