15 citations · 86 across the 50 of their papers we have counts for
6 papers · 1 filter
Partition-free families of sets
Peter Frankl, Andrey Kupavskii
Let denote the maximum size of a family of subsets which does not contain two disjoint sets along with their union. In 1968 Kleitman proved that $m(n) = {n\choose m+1}+\ldot…
Families of vectors without antipodal pairs
Peter Frankl, Andrey Kupavskii
Some Erdős-Ko-Rado type extremal properties of families of vectors from are considered.
A degree version of the Hilton--Milner theorem
Peter Frankl, Jie Han, Hao Huang +1
An intersecting family of sets is trivial if all of its members share a common element. Hilton and Milner proved a strong stability result for the celebrated Erdős--Ko--Rado theore…
Borsuk and Ramsey type questions in Euclidean space
Peter Frankl, János Pach, Christian Reiher +1
We give a short survey of problems and results on (1) diameter graphs and hypergraphs, and (2) geometric Ramsey theory. We also make some modest contributions to both areas. Extend…
Counting intersecting and pairs of cross-intersecting families
Peter Frankl, Andrey Kupavskii
A family of subsets of is called {\it intersecting} if any two of its sets intersect. A classical result in extremal combinatorics due to Erdős, Ko, and Rado deter…
Families of sets with no matchings of sizes 3 and 4
Peter Frankl, Andrey Kupavskii
In this paper, we study the following classical question of extremal set theory: what is the maximum size of a family of subsets of such that no sets from the family are…