8 citations · 65 across the 30 of their papers we have counts for
24 papers · 1 filter
Overlap-Helly theorems
Andreas F. Holmsen, Alfredo Hubard
In this paper we introduce a generalization of Helly's theorem closely connected to Bárány-Gromov overlap theorems (also called selection lemmas). Our main result implies both the…
Clique number and triangle densities in -free graphs
Gunnar Fløystad, Andreas F. Holmsen
For a -free graph on vertices --- one with no induced cycle on four vertices --- we study the two-sided extremal problem for the triangle density : How large and ho…
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 fo…
Piercing all maximum cliques in hypergraphs
Andreas Holmsen, Attila Jung, Balázs Keszegh +2
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…
A topological product Tverberg Theorem
Andreas F. Holmsen, Grace McCourt, Daniel McGinnis +1
We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let denote the 8-dimensional simplex viewed as an a…
The fractional Helly number for separable convexity spaces
Andreas F. Holmsen, Zuzana Patáková
A convex lattice set in is the intersection of a convex set in with the integer lattice . A classical theorem of Doignon states that the…