TY - JOUR

T1 - On the intersection of infinite matroids

AU - Aigner-Horev, Elad

AU - Carmesin, Johannes

AU - Fröhlich, Jan Oliver

N1 - Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/6

Y1 - 2018/6

N2 - We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009. We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids. In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.

AB - We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009. We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids. In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.

KW - Infinite graphs

KW - Infinite matroids

KW - Matroid intersection

UR - http://www.scopus.com/inward/record.url?scp=85044170777&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2018.02.018

DO - 10.1016/j.disc.2018.02.018

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AN - SCOPUS:85044170777

SN - 0012-365X

VL - 341

SP - 1582

EP - 1596

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 6

ER -