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 -