Infinite Graphic Matroids
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Bowler, N., Carmesin, J., & Christian, R. (2018). Infinite Graphic Matroids. Combinatorica, 38 (2), 305-339. https://doi.org/10.1007/s00493-016-3178-3
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.
External DOI: https://doi.org/10.1007/s00493-016-3178-3
This record's URL: https://www.repository.cam.ac.uk/handle/1810/265864