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

Department of Computer Science

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

3 Scopus citations

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	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 - Jan 2016

Keywords

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

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10.1016/j.jctb.2015.05.011

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The structure of 2-separations of infinite matroids

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Keywords

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