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…
Stability with minuscule structure for chromatic thresholds
Jaehoon Kim, Hong Liu, Chong Shangguan +3
The chromatic threshold of a graph is the infimum of such that the chromatic number of every -vertex -free graph with minimum degree at least is bo…
On the order of intersecting hypergraphs
Stijn Cambie, Jaehoon Kim, Hyunwoo Lee +2
Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In…
Isodiametric inequality for vector spaces
Jiaqi Liao, Hong Liu, Guiying Yan
A theorem of Kleitman states that a collection of binary vectors with diameter d has cardinality at most that of a Hamming ball of radius d/2. In this paper, we give a q-analog of…
Extremal density for subdivisions with length or sparsity constraints
Jaehoon Kim, Hong Liu, Yantao Tang +3
Given a graph , a balanced subdivision of is obtained by replacing all edges of with internally disjoint paths of the same length. In this paper, we prove that for any g…