Decomposing infinite matroids into their 3-connected minors

Elad Aigner-Horev; Reinhard Diestel; Luke Postle

doi:10.1016/j.endm.2011.09.003

Decomposing infinite matroids into their 3-connected minors

Elad Aigner-Horev, Reinhard Diestel, Luke Postle

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Pages (from-to)	11-16
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	38
DOIs	https://doi.org/10.1016/j.endm.2011.09.003
State	Published - 1 Dec 2011
Externally published	Yes

Keywords

Decomposition trees
Infinite matroids
Matroid connectivity

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.endm.2011.09.003

Cite this

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AU - Diestel, Reinhard

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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

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DO - 10.1016/j.endm.2011.09.003

M3 - Article

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EP - 16

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Decomposing infinite matroids into their 3-connected minors

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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