The Highly Connected Matroids in Minor-Closed Classes

For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.

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Bibliographic Details
Published in:Annals of combinatorics 2015-03, Vol.19 (1), p.107-123
Main Authors: Geelen, Jim, Gerards, Bert, Whittle, Geoff
Format: Article
Language:English
Subjects:
Combinatorics
Mathematics
Mathematics and Statistics
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Description
Summary:For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-015-0251-3