6 papers
Global and local degree conditions for matchability
Ron Aharoni, Eli Berger, Attila Joó
A corollary of Hall's marriage theorem is that a sufficient condition for a list of sets to have a system of distinct representatives is that $|V_i|\ge deg_{\{…
Hindrance from a wasteful partial linkage
Attila Joó
Let be a (possibly infinite) digraph and . A hindrance consists of an -separator together with a set of disjoint -paths linking a pr…
A Note on Matching Variables to Equations
Attila Joó
We showed with J. P. Gollin that if a (possibly infinite) homogeneous linear equation system has only the trivial solution, then there exists an injective function from the variabl…
The Lovász-Cherkassky theorem in infinite graphs
Attila Joó
Infinite generalizations of theorems in finite combinatorics were initiated by Erdős due to his famous Erdős-Menger conjecture (now known as the Aharoni-Berger theorem) that extend…
Weakly reflecting graph properties
Attila Joó
L. Soukup formulated an abstract framework in his introductory paper for proving theorems about uncountable graphs by subdividing them by an increasing continuous chain of elementa…
Finite matchability under the matroidal Hall's condition
Attila Joó
Aharoni and Ziv conjectured that if and are finitary matroids on , then a certain ``Hall-like'' condition is sufficient to guarantee the existence of an -inde…