5 papers
Strong invariants and Tverberg numbers in convexity spaces
Minho Cho, Andreas F. Holmsen, Attila Jung +1
Helly, Carathéodory, and Radon numbers encode three kinds of finite certificates in a convexity space: for the emptiness of an intersection, for membership in a convex hull, and f…
Piercing all maximum cliques in hypergraphs
Andreas Holmsen, Attila Jung, Balázs Keszegh +5
Graphs whose maximum clique size exceeds half of the total number of vertices satisfy a classical property: the family of their maximum sized cliques can be pierced by a single ver…
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…
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…
The Quantitative Fractional Helly theorem
Nóra Frankl, Attila Jung, István Tomon
Two celebrated extensions of Helly's theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Bárány, Katchalski, and Pach (19…