3 papers
math.CO2025
Helly-type theorems for monotone properties of boxes
Nóra Frankl, Attila Jung
We present a unified approach to prove Helly-type theorems for monotone properties of boxes, such as having large volume or containing points from a given set. As a corollary, we o…
math.CO2024
A note on infinite versions of -theorems
Attila Jung, Dömötör Pálvölgyi
We prove that fractional Helly and -theorems imply -theorems in an entirely abstract setting. We give a plethora of applications, including reproving almost al…
math.CO2023
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…