[HTML][HTML] Proof of Nash-Williams' intersection conjecture for countable matroids

A Joó - Advances in Mathematics, 2021 - Elsevier
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= EM∪ EN for which I∩ …

[HTML][HTML] A Cantor-Bernstein-type theorem for spanning trees in infinite graphs

J Erde, JP Gollin, A Joó, P Knappe, M Pitz - Journal of Combinatorial Theory …, 2021 - Elsevier
We show that if a graph admits a packing and a covering both consisting of λ many spanning
trees, where λ is some infinite cardinal, then the graph also admits a decomposition into λ …

On generalisations of the Aharoni–Pouzet base exchange theorem

Z Jankó, A Joó - Bulletin of the London Mathematical Society, 2023 - Wiley Online Library
Abstract The Greene–Magnanti theorem states that if MM is a finite matroid, B 0 B_0 and B 1
B_1 are bases and B 0=⋃ i= 1 n X i B_0=⋃_i=1^nX_i is a partition, then there is a partition B …

On the packing/covering conjecture of infinite matroids

A Joó - Israel Journal of Mathematics, 2024 - Springer
Abstract The Packing/Covering Conjecture was introduced by Bowler and Carmesin
motivated by the Matroid Partition Theorem of Edmonds and Fulkerson. A packing for a …

[HTML][HTML] Intersection of a partitional and a general infinite matroid

A Joó - Discrete Mathematics, 2021 - Elsevier
Let E be a possibly infinite set and let M and N be matroids defined on E. We say that the
pair {M, N} has the Intersection property if M and N share an independent set I admitting a …

A Cantor-Bernstein theorem for infinite matroids

A Joó - arxiv preprint arxiv:2009.08439, 2020 - arxiv.org
arxiv:2009.08439v4 [math.CO] 9 May 2022 Page 1 A CANTOR-BERNSTEIN THEOREM FOR
INFINITE MATROIDS ATTILA JOÓ Abstract. We give a common matroidal generalisation of ‘A …