2 citations · 3 across the 4 of their papers we have counts for
5 papers
The VC dimension of partial concept classes via Radon's theorem
Grigory Ivanov, Attila Jung, Márton Naszódi
Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concept…
Quantitative Helly-type Theorems via Hypergraph Chains
Attila Jung
We propose a combinatorial framework to analyze quantitative Helly-type questions. Using this framework, we prove a Quantitative Fractional Helly Theorem with Fractional Helly Numb…
On Helly numbers of exponential lattices
Gergely Ambrus, Martin Balko, Nóra Frankl +2
Given a set , define the \emph{Helly number of }, denoted by , as the smallest positive integer , if it exists, for which the following statem…
Shadow of Hypergraphs with Bounded Degree
Attila Jung
We study the size of the shadow of -uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a fu…
Quantitative Fractional Helly and -Theorems
Attila Jung, Márton Naszódi
We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main geometri…