The structure of 2-separations of infinite matroids

Elad Aigner-Horev; Reinhard Diestel; Luke Postle

doi:10.1016/j.jctb.2015.05.011

The structure of 2-separations of infinite matroids

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 nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits, and the edges of T correspond to certain nested 2-separations of M. These decompositions are invariant under duality.

Original language	American English
Pages (from-to)	25-56
Number of pages	32
Journal	Journal of Combinatorial Theory. Series B
Volume	116
DOIs	https://doi.org/10.1016/j.jctb.2015.05.011
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

2-separation
3-connected
Cunningham
Edmonds
Infinite
Matroid
Seymour
Tree-decomposition
Tutte

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2015.05.011

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

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AU - Diestel, Reinhard

AU - Postle, Luke

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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 nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits, and the edges of T correspond to certain nested 2-separations of M. These decompositions are invariant under duality.

KW - 2-separation

KW - 3-connected

KW - Cunningham

KW - Edmonds

KW - Infinite

KW - Matroid

KW - Seymour

KW - Tree-decomposition

KW - Tutte

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DO - 10.1016/j.jctb.2015.05.011

M3 - Article

SN - 0095-8956

VL - 116

SP - 25

EP - 56

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

The structure of 2-separations of infinite matroids

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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