Proof of Nash-Williams' Intersection Conjecture for countable matroids

2019/12/31 by Attila Joó, Joó, Attila
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1912.13253

arxiv created 2021/04/04 · arxiv updated 2021/04/06

Abstract

We prove that if M and N are finitary matroids on a common countable edge set E then they admit a common independent set I such that there is a bipartition E=E_M∪ E_N for which I∩ E_M spans E_M in M and I∩ E_N spans E_N in N . It answers positively the Matroid Intersection Conjecture of Nash-Williams in the countable case.

Related

• Intersection of a partitional and a general infinite matroid
• The matroid intersection conjecture
• On the intersection of infinite matroids
• Finite matchability under the matroidal Hall's condition
• On the Packing/Covering Conjecture of Infinite Matroids