1 citations · 3 across the 14 of their papers we have counts for
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Matching variables to equations in infinite linear equation systems
J. Pascal Gollin, Attila Joó
A fundamental result in linear algebra states that if a homogenous linear equation system has only the trivial solution, then there are at most as many variables as equations. We p…
On generalisations of the Aharoni-Pouzet base exchange theorem
Zsuzsanna Jankó, Attila Joó
The Greene-Magnanti theorem states that if is a finite matroid, and are bases and is a partition, then there is a partition $ B_…
Maker-Breaker games on and
Nathan Bowler, Florian Gut, Attila Joó +1
We investigate Maker-Breaker games on graphs of size in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the gam…
The Lovász-Cherkassky theorem for locally finite graphs with ends
Raphael W. Jacobs, Attila Joó, Paul Knappe +2
Lovász and Cherkassky discovered independently that, if is a finite graph and such that the degree is even for every vertex , t…
Cutting a cake for infinitely many guests
Zsuzsanna Jankó, Attila Joó
Fair division with unequal shares is an intensively studied recourse allocation problem. For , let be an atomless probability measure on the measurable space $(…
Large vertex-flames in uncountable digraphs
Florian Gut, Attila Joó
The study of minimal subgraphs witnessing a connectivity property is an important field in graph theory. The foundation for large flames has been laid by Lovász: Let be…
On the Packing/Covering Conjecture of Infinite Matroids
Attila Joó
The Packing/Covering Conjecture was introduced by Bowler and Carmesin motivated by the Matroid Partition Theorem by Edmonds and Fulkerson. A packing for a family o…
The Lovász-Cherkassky theorem in countable graphs
Attila Joó
Lovász and Cherkassky discovered in the 1970s independently that if is a finite graph with a given set of terminal vertices such that is inner Eulerian, then the…
A Cantor-Bernstein theorem for infinite matroids
Attila Joó
We give a common matroidal generalisation of `A Cantor-Bernstein theorem for paths in graphs' by Diestel and Thomassen and `A Cantor-Bernstein-type theorem for spanning trees in in…
Intersection of a partitional and a general infinite matroid
Attila Joó
Let be a possibly infinite set and let and be matroids defined on . We say that the pair has the Intersection property if and share…
Greedoids from flames
Attila Joó
A digraph with is an -flame if for every , the in-degree of is equal to the local edge-connectivity . We show that for e…
Enlarging vertex-flames in countable digraphs
Joshua Erde, J. Pascal Gollin, Attila Joó
A rooted digraph is a vertex-flame if for every vertex there is a set of internally disjoint directed paths from the root to whose set of terminal edges covers all ingoing…
Proof of Nash-Williams' Intersection Conjecture for countable matroids
Attila Joó
We prove that if and are finitary matroids on a common countable edge set then they admit a common independent set such that there is a bipartition $ E=E_{M}…
Reducing the dichromatic number via cycle reversions in infinite digraphs
Paul Ellis, Attila Joó, Dániel T. Soukup
We prove the following conjecture of S. Thomassé: for every (potentially infinite) digraph it is possible to iteratively reverse directed cycles in such a way that the dichro…
On the growth rate of dichromatic numbers of finite subdigraphs
Attila Joó
Chris Lambie-Hanson proved recently that for every function there is an -chromatic graph of size such that…
Uncountable dichromatic number without short directed cycles
Attila Joó
A. Hajnal and P. Erdős proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example (among other obligatory subgraphs). It w…
The Complete Lattice of Erdős-Menger Separations
Attila Joó
F. Escalante and T. Gallai studied in the seventies the structure of different kind of separations and cuts between a vertex pair in a (possibly infinite) graph. One of their resul…
Vertex-flames in countable rooted digraphs preserving an Erdős-Menger separation for each vertex
Attila Joó
It follows from a theorem of Lovász that if is a finite digraph with then there is a spanning subdigraph of such that for every vertex t…
Independent and maximal branching packing in infinite matroid-rooted digraphs
Attila Joó
We prove a common generalization of the maximal independent arborescence packing theorem of Cs. Király and two of our earlier works about packing branchings in infinite digraphs.
T-joins in infinite graphs as edge-disjoint system of paths matching the vertices in
Attila Joó
We characterize the class of infinite connected graphs for which there exists a -join for any choice of an infinite . We also show that the following…
On partitioning the edges of an infinite digraph into directed cycles
Attila Joó
Nash-Williams proved that for an undirected graph the set can be partitioned into cycles if and only if every cut has either even or infinite number of edges. Later…