TY - JOUR
T1 - Decomposing infinite matroids into their 3-connected minors
AU - Aigner-Horev, Elad
AU - Diestel, Reinhard
AU - Postle, Luke
N1 - Funding Information:
[email protected], Mathematics Department, Hamburg University. Supported by the Minerva foundation 2 [email protected], School of Mathematics, Georgia Institute of Technology. Partially supported by a NSF Graduate Research Fellowship.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - Generalizing a well-known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the vertices of T correspond to minors of M each of which is either a maximal 3-connected minor of M, a circuit or a cocircuit, and the edges of T correspond to certain 2-separations of M. In addition, we show that the decomposition of M determines the decomposition of its dual in a natural manner.
AB - Generalizing a well-known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the vertices of T correspond to minors of M each of which is either a maximal 3-connected minor of M, a circuit or a cocircuit, and the edges of T correspond to certain 2-separations of M. In addition, we show that the decomposition of M determines the decomposition of its dual in a natural manner.
KW - Decomposition trees
KW - Infinite matroids
KW - Matroid connectivity
UR - http://www.scopus.com/inward/record.url?scp=82955245659&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2011.09.003
DO - 10.1016/j.endm.2011.09.003
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AN - SCOPUS:82955245659
SN - 1571-0653
VL - 38
SP - 11
EP - 16
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -