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	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

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title = "Decomposing infinite matroids into their 3-connected minors",

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.",

keywords = "Decomposition trees, Infinite matroids, Matroid connectivity",

author = "Elad Aigner-Horev and Reinhard Diestel and Luke Postle",

note = "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.",

year = "2011",

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doi = "10.1016/j.endm.2011.09.003",

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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

M3 - مقالة

SN - 1571-0653

VL - 38

SP - 11

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

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