Infinite Graphic Matroids
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Bowler, N
Carmesin, J
Christian, R
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. Working in the representing space, we prove that any circuit in a 3-connected graphic matroid is countable.
Description
Keywords
4901 Applied Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Combinatorica
Conference Name
Journal ISSN
0209-9683
1439-6912
1439-6912
Volume Title
38
Publisher
Springer Science and Business Media LLC